5x-11=(x^2)-3x-4

Solution for 5x-11=(x^2)-3x-4 equation:

5x-11=(x^2)-3x-4

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+8x-7=0

a = -1; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·(-1)·(-7)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*-1}=\frac{-2}{-2}
=1
$