25x^2+80x=-61

Solution for 25x^2+80x=-61 equation:

25x^2+80x=-61

We move all terms to the left:

25x^2+80x-(-61)=0

We add all the numbers together, and all the variables

25x^2+80x+61=0

a = 25; b = 80; c = +61;
Δ = b2-4ac
Δ = 802-4·25·61
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{-(80)-10\sqrt{3}}{2*25}=\frac{-80-10\sqrt{3}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+10\sqrt{3}}{2*25}=\frac{-80+10\sqrt{3}}{50}
$