(x+4)(x-3)=5x-11

Solution for (x+4)(x-3)=5x-11 equation:

(x+4)(x-3)=5x-11

We move all terms to the left:

(x+4)(x-3)-(5x-11)=0

We get rid of parentheses

(x+4)(x-3)-5x+11=0

We multiply parentheses ..

(+x^2-3x+4x-12)-5x+11=0

We get rid of parentheses

x^2-3x+4x-5x-12+11=0

We add all the numbers together, and all the variables

x^2-4x-1=0

a = 1; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·1·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{5}}{2*1}=\frac{4-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{5}}{2*1}=\frac{4+2\sqrt{5}}{2}
$