20x+x^2=-25

Solution for 20x+x^2=-25 equation:

20x+x^2=-25

We move all terms to the left:

20x+x^2-(-25)=0

We add all the numbers together, and all the variables

x^2+20x+25=0

a = 1; b = 20; c = +25;
Δ = b2-4ac
Δ = 202-4·1·25
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{3}}{2*1}=\frac{-20-10\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{3}}{2*1}=\frac{-20+10\sqrt{3}}{2}
$