11x*x-8x=11

Solution for 11x*x-8x=11 equation:

11x*x-8x=11

We move all terms to the left:

11x*x-8x-(11)=0

We add all the numbers together, and all the variables

-8x+11x*x-11=0

Wy multiply elements

11x^2-8x-11=0

a = 11; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·11·(-11)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{137}}{2*11}=\frac{8-2\sqrt{137}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{137}}{2*11}=\frac{8+2\sqrt{137}}{22}
$