4x2+100x=-100

Solution for 4x2+100x=-100 equation:

4x^2+100x=-100

We move all terms to the left:

4x^2+100x-(-100)=0

We add all the numbers together, and all the variables

4x^2+100x+100=0

a = 4; b = 100; c = +100;
Δ = b2-4ac
Δ = 1002-4·4·100
Δ = 8400
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:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{21}}{2*4}=\frac{-100-20\sqrt{21}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{21}}{2*4}=\frac{-100+20\sqrt{21}}{8}
$