10x^2+2x=50

Solution for 10x^2+2x=50 equation:

10x^2+2x=50

We move all terms to the left:

10x^2+2x-(50)=0

a = 10; b = 2; c = -50;
Δ = b2-4ac
Δ = 22-4·10·(-50)
Δ = 2004
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:

$\sqrt{\Delta}=\sqrt{2004}=\sqrt{4*501}=\sqrt{4}*\sqrt{501}=2\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{501}}{2*10}=\frac{-2-2\sqrt{501}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{501}}{2*10}=\frac{-2+2\sqrt{501}}{20}
$