x(x-8)=3x+7

Solution for x(x-8)=3x+7 equation:

x(x-8)=3x+7

We move all terms to the left:

x(x-8)-(3x+7)=0

We multiply parentheses

x^2-8x-(3x+7)=0

We get rid of parentheses

x^2-8x-3x-7=0

We add all the numbers together, and all the variables

x^2-11x-7=0

a = 1; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·1·(-7)
Δ = 149
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{-(-11)-\sqrt{149}}{2*1}=\frac{11-\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{149}}{2*1}=\frac{11+\sqrt{149}}{2}
$