50x^2+25x=125

Solution for 50x^2+25x=125 equation:

50x^2+25x=125

We move all terms to the left:

50x^2+25x-(125)=0

a = 50; b = 25; c = -125;
Δ = b2-4ac
Δ = 252-4·50·(-125)
Δ = 25625
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:

$\sqrt{\Delta}=\sqrt{25625}=\sqrt{625*41}=\sqrt{625}*\sqrt{41}=25\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25\sqrt{41}}{2*50}=\frac{-25-25\sqrt{41}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25\sqrt{41}}{2*50}=\frac{-25+25\sqrt{41}}{100}
$