5+8x-4x^2=-5x

Solution for 5+8x-4x^2=-5x equation:

5+8x-4x^2=-5x

We move all terms to the left:

5+8x-4x^2-(-5x)=0

We get rid of parentheses

-4x^2+8x+5x+5=0

We add all the numbers together, and all the variables

-4x^2+13x+5=0

a = -4; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·(-4)·5
Δ = 249
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{-(13)-\sqrt{249}}{2*-4}=\frac{-13-\sqrt{249}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{249}}{2*-4}=\frac{-13+\sqrt{249}}{-8}
$