11x^2-8x=4x+3

Solution for 11x^2-8x=4x+3 equation:

11x^2-8x=4x+3

We move all terms to the left:

11x^2-8x-(4x+3)=0

We get rid of parentheses

11x^2-8x-4x-3=0

We add all the numbers together, and all the variables

11x^2-12x-3=0

a = 11; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·11·(-3)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{69}}{2*11}=\frac{12-2\sqrt{69}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{69}}{2*11}=\frac{12+2\sqrt{69}}{22}
$