Question

1. $-3x^2 + 8x = -10$

Explanation:

Step1: Rewrite to standard quadratic form

Add 10 to both sides:
$ -3x^2 + 8x + 10 = 0 $
Multiply by -1 to simplify:
$ 3x^2 - 8x - 10 = 0 $

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=3$, $b=-8$, $c=-10$

Step3: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$x=\frac{-(-8)\pm\sqrt{(-8)^2-4(3)(-10)}}{2(3)}$

Step4: Calculate discriminant

Compute $b^2-4ac$:
$(-8)^2-4(3)(-10)=64+120=184$

Step5: Simplify the expression

Simplify $\sqrt{184}=2\sqrt{46}$, so:
$x=\frac{8\pm2\sqrt{46}}{6}=\frac{4\pm\sqrt{46}}{3}$

Answer:

$x=\frac{4+\sqrt{46}}{3}$ and $x=\frac{4-\sqrt{46}}{3}$