(x-7)(x-3)+10x=30

Solution for (x-7)(x-3)+10x=30 equation:

(x-7)(x-3)+10x=30

We move all terms to the left:

(x-7)(x-3)+10x-(30)=0

We add all the numbers together, and all the variables

10x+(x-7)(x-3)-30=0

We multiply parentheses ..

(+x^2-3x-7x+21)+10x-30=0

We get rid of parentheses

x^2-3x-7x+10x+21-30=0

We add all the numbers together, and all the variables

x^2-9=0

a = 1; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·1·(-9)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*1}=\frac{6}{2}
=3
$