20x=-4x^2-23

Solution for 20x=-4x^2-23 equation:

20x=-4x^2-23

We move all terms to the left:

20x-(-4x^2-23)=0

We get rid of parentheses

4x^2+20x+23=0

a = 4; b = 20; c = +23;
Δ = b2-4ac
Δ = 202-4·4·23
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{2}}{2*4}=\frac{-20-4\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{2}}{2*4}=\frac{-20+4\sqrt{2}}{8}
$