11x2-5x=50

Solution for 11x2-5x=50 equation:

11x^2-5x=50

We move all terms to the left:

11x^2-5x-(50)=0

a = 11; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·11·(-50)
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{89}}{2*11}=\frac{5-5\sqrt{89}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{89}}{2*11}=\frac{5+5\sqrt{89}}{22}
$