(x-5)(x+2)=7x

Solution for (x-5)(x+2)=7x equation:

(x-5)(x+2)=7x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+x^2+2x-5x-10)-7x=0

We get rid of parentheses

x^2+2x-5x-7x-10=0

We add all the numbers together, and all the variables

x^2-10x-10=0

a = 1; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·1·(-10)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{35}}{2*1}=\frac{10-2\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{35}}{2*1}=\frac{10+2\sqrt{35}}{2}
$