7x-8=-3x^2

Solution for 7x-8=-3x^2 equation:

7x-8=-3x^2

We move all terms to the left:

7x-8-(-3x^2)=0

We get rid of parentheses

3x^2+7x-8=0

a = 3; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·3·(-8)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{145}}{2*3}=\frac{-7-\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*3}=\frac{-7+\sqrt{145}}{6}
$