x^2-11x+56=5x+13

Solution for x^2-11x+56=5x+13 equation:

x^2-11x+56=5x+13

We move all terms to the left:

x^2-11x+56-(5x+13)=0

We get rid of parentheses

x^2-11x-5x-13+56=0

We add all the numbers together, and all the variables

x^2-16x+43=0

a = 1; b = -16; c = +43;
Δ = b2-4ac
Δ = -162-4·1·43
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{21}}{2*1}=\frac{16-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{21}}{2*1}=\frac{16+2\sqrt{21}}{2}
$