-3x^2+14x-8=0 15^2-23times 4u=0 10x^2+11x-6=0 -4times 2-8x+6=0 6x+10x+3=0

Mari kita selesaikan setiap persamaan satu per satu.

1. Persamaan Kuadrat:
\[
-3x^{2} + 14x - 8 = 0
\]
Untuk menyelesaikan persamaan kuadrat \(ax^2 + bx + c = 0\), kita gunakan rumus kuadrat:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Di sini, \(a = -3\), \(b = 14\), dan \(c = -8\).

\[
x = \frac{-14 \pm \sqrt{14^2 - 4(-3)(-8)}}{2(-3)}
\]
\[
x = \frac{-14 \pm \sqrt{196 - 96}}{-6}
\]
\[
x = \frac{-14 \pm \sqrt{100}}{-6}
\]
\[
x = \frac{-14 \pm 10}{-6}
\]

Jadi, solusinya adalah:
\[
x = \frac{-14 + 10}{-6} = \frac{-4}{-6} = \frac{2}{3}
\]
dan
\[
x = \frac{-14 - 10}{-6} = \frac{-24}{-6} = 4
\]

2. Persamaan Linier:
\[
15^2 - 23 \times 4u = 0
\]
\[
225 - 92u = 0
\]
\[
92u = 225
\]
\[
u = \frac{225}{92}
\]

3. Persamaan Kuadrat:
\[
10x^{2} + 11x - 6 = 0
\]
Menggunakan rumus kuadrat dengan \(a = 10\), \(b = 11\), dan \(c = -6\):
\[
x = \frac{-11 \pm \sqrt{11^2 - 4(10)(-6)}}{2(10)}
\]
\[
x = \frac{-11 \pm \sqrt{121 + 240}}{20}
\]
\[
x = \frac{-11 \pm \sqrt{361}}{20}
\]
\[
x = \frac{-11 \pm 19}{20}
\]

Jadi, solusinya adalah:
\[
x = \frac{-11 + 19}{20} = \frac{8}{20} = \frac{2}{5}
\]
dan
\[
x = \frac{-11 - 19}{20} = \frac{-30}{20} = -\frac{3}{2}
\]

4. Persamaan Linier:
\[
-4 \times 2 - 8x + 6 = 0
\]
\[
-8 - 8x + 6 = 0
\]
\[
-8x - 2 = 0
\]
\[
-8x = 2
\]
\[
x = -\frac{2}{8} = -\frac{1}{4}
\]

5. Persamaan Linier:
\[
6x + 10x + 3 = 0
\]
\[
16x + 3 = 0
\]
\[
16x = -3
\]
\[
x = -\frac{3}{16}
\]

Jadi, solusi untuk setiap persamaan adalah:
1. \(x = \frac{2}{3}\) atau \(x = 4\)
2. \(u = \frac{225}{92}\)
3. \(x = \frac{2}{5}\) atau \(x = -\frac{3}{2}\)
4. \(x = -\frac{1}{4}\)
5. \(x = -\frac{3}{16}\)