X^2-4x=5x+11

Solution for X^2-4x=5x+11 equation:

X^2-4X=5X+11

We move all terms to the left:

X^2-4X-(5X+11)=0

We get rid of parentheses

X^2-4X-5X-11=0

We add all the numbers together, and all the variables

X^2-9X-11=0

a = 1; b = -9; c = -11;
Δ = b2-4ac
Δ = -92-4·1·(-11)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5\sqrt{5}}{2*1}=\frac{9-5\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5\sqrt{5}}{2*1}=\frac{9+5\sqrt{5}}{2}
$