X-4x+11(x+11)(x-4)=34

Solution for X-4x+11(x+11)(x-4)=34 equation:

X-4X+11(X+11)(X-4)=34

We move all terms to the left:

X-4X+11(X+11)(X-4)-(34)=0

We add all the numbers together, and all the variables

-3X+11(X+11)(X-4)-34=0

We multiply parentheses ..

11(+X^2-4X+11X-44)-3X-34=0

We multiply parentheses

11X^2-44X+121X-3X-484-34=0

We add all the numbers together, and all the variables

11X^2+74X-518=0

a = 11; b = 74; c = -518;
Δ = b2-4ac
Δ = 742-4·11·(-518)
Δ = 28268
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:

$\sqrt{\Delta}=\sqrt{28268}=\sqrt{4*7067}=\sqrt{4}*\sqrt{7067}=2\sqrt{7067}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-2\sqrt{7067}}{2*11}=\frac{-74-2\sqrt{7067}}{22}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+2\sqrt{7067}}{2*11}=\frac{-74+2\sqrt{7067}}{22}
$