5x-8=-2x^2

Solution for 5x-8=-2x^2 equation:

5x-8=-2x^2

We move all terms to the left:

5x-8-(-2x^2)=0

We get rid of parentheses

2x^2+5x-8=0

a = 2; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·2·(-8)
Δ = 89
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{-(5)-\sqrt{89}}{2*2}=\frac{-5-\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*2}=\frac{-5+\sqrt{89}}{4}
$