20x=-2x^2-48

Solution for 20x=-2x^2-48 equation:

20x=-2x^2-48

We move all terms to the left:

20x-(-2x^2-48)=0

We get rid of parentheses

2x^2+20x+48=0

a = 2; b = 20; c = +48;
Δ = b2-4ac
Δ = 202-4·2·48
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4}{2*2}=\frac{-16}{4}
=-4
$