25x^2+100x=-10

Solution for 25x^2+100x=-10 equation:

25x^2+100x=-10

We move all terms to the left:

25x^2+100x-(-10)=0

We add all the numbers together, and all the variables

25x^2+100x+10=0

a = 25; b = 100; c = +10;
Δ = b2-4ac
Δ = 1002-4·25·10
Δ = 9000
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:

$\sqrt{\Delta}=\sqrt{9000}=\sqrt{900*10}=\sqrt{900}*\sqrt{10}=30\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-30\sqrt{10}}{2*25}=\frac{-100-30\sqrt{10}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+30\sqrt{10}}{2*25}=\frac{-100+30\sqrt{10}}{50}
$