11x2-10x=23

Solution for 11x2-10x=23 equation:

11x^2-10x=23

We move all terms to the left:

11x^2-10x-(23)=0

a = 11; b = -10; c = -23;
Δ = b2-4ac
Δ = -102-4·11·(-23)
Δ = 1112
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:

$\sqrt{\Delta}=\sqrt{1112}=\sqrt{4*278}=\sqrt{4}*\sqrt{278}=2\sqrt{278}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{278}}{2*11}=\frac{10-2\sqrt{278}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{278}}{2*11}=\frac{10+2\sqrt{278}}{22}
$