x^2+20x+70=-5

Solution for x^2+20x+70=-5 equation:

x^2+20x+70=-5

We move all terms to the left:

x^2+20x+70-(-5)=0

We add all the numbers together, and all the variables

x^2+20x+75=0

a = 1; b = 20; c = +75;
Δ = b2-4ac
Δ = 202-4·1·75
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10}{2*1}=\frac{-10}{2}
=-5
$