(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+6x-1=0

a = 1; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·1·(-1)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{10}}{2*1}=\frac{-6-2\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{10}}{2*1}=\frac{-6+2\sqrt{10}}{2}
$