x+7=x^2-3x-4

Solution for x+7=x^2-3x-4 equation:

x+7=x^2-3x-4

We move all terms to the left:

x+7-(x^2-3x-4)=0

We get rid of parentheses

-x^2+x+3x+4+7=0

We add all the numbers together, and all the variables

-1x^2+4x+11=0

a = -1; b = 4; c = +11;
Δ = b2-4ac
Δ = 42-4·(-1)·11
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{15}}{2*-1}=\frac{-4-2\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{15}}{2*-1}=\frac{-4+2\sqrt{15}}{-2}
$