25x^2+80x=-62

Solution for 25x^2+80x=-62 equation:

25x^2+80x=-62

We move all terms to the left:

25x^2+80x-(-62)=0

We add all the numbers together, and all the variables

25x^2+80x+62=0

a = 25; b = 80; c = +62;
Δ = b2-4ac
Δ = 802-4·25·62
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-10\sqrt{2}}{2*25}=\frac{-80-10\sqrt{2}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+10\sqrt{2}}{2*25}=\frac{-80+10\sqrt{2}}{50}
$