11x^2-12x-10=18x+10

Solution for 11x^2-12x-10=18x+10 equation:

11x^2-12x-10=18x+10

We move all terms to the left:

11x^2-12x-10-(18x+10)=0

We get rid of parentheses

11x^2-12x-18x-10-10=0

We add all the numbers together, and all the variables

11x^2-30x-20=0

a = 11; b = -30; c = -20;
Δ = b2-4ac
Δ = -302-4·11·(-20)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{445}}{2*11}=\frac{30-2\sqrt{445}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{445}}{2*11}=\frac{30+2\sqrt{445}}{22}
$