(x+5)(x-3)=7x

Solution for (x+5)(x-3)=7x equation:

(x+5)(x-3)=7x

We move all terms to the left:

(x+5)(x-3)-(7x)=0

We add all the numbers together, and all the variables

-7x+(x+5)(x-3)=0

We multiply parentheses ..

(+x^2-3x+5x-15)-7x=0

We get rid of parentheses

x^2-3x+5x-7x-15=0

We add all the numbers together, and all the variables

x^2-5x-15=0

a = 1; b = -5; c = -15;
Δ = b2-4ac
Δ = -52-4·1·(-15)
Δ = 85
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{-(-5)-\sqrt{85}}{2*1}=\frac{5-\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*1}=\frac{5+\sqrt{85}}{2}
$