8x=5-4x^2

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

8x=5-4x^2

We move all terms to the left:

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

We get rid of parentheses

4x^2+8x-5=0

a = 4; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·4·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*4}=\frac{4}{8}
=1/2
$