x^2-13-11=-7x+5

Solution for x^2-13-11=-7x+5 equation:

x^2-13-11=-7x+5

We move all terms to the left:

x^2-13-11-(-7x+5)=0

We add all the numbers together, and all the variables

x^2-(-7x+5)-24=0

We get rid of parentheses

x^2+7x-5-24=0

We add all the numbers together, and all the variables

x^2+7x-29=0

a = 1; b = 7; c = -29;
Δ = b2-4ac
Δ = 72-4·1·(-29)
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{165}}{2*1}=\frac{-7-\sqrt{165}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{165}}{2*1}=\frac{-7+\sqrt{165}}{2}
$