5x^2-2x=50

Solution for 5x^2-2x=50 equation:

5x^2-2x=50

We move all terms to the left:

5x^2-2x-(50)=0

a = 5; b = -2; c = -50;
Δ = b2-4ac
Δ = -22-4·5·(-50)
Δ = 1004
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:

$\sqrt{\Delta}=\sqrt{1004}=\sqrt{4*251}=\sqrt{4}*\sqrt{251}=2\sqrt{251}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{251}}{2*5}=\frac{2-2\sqrt{251}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{251}}{2*5}=\frac{2+2\sqrt{251}}{10}
$