(7x-5x)(2x-5)=150

Solution for (7x-5x)(2x-5)=150 equation:

(7x-5x)(2x-5)=150

We move all terms to the left:

(7x-5x)(2x-5)-(150)=0

We add all the numbers together, and all the variables

(+2x)(2x-5)-150=0

We multiply parentheses ..

(+4x^2-10x)-150=0

We get rid of parentheses

4x^2-10x-150=0

a = 4; b = -10; c = -150;
Δ = b2-4ac
Δ = -102-4·4·(-150)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-50}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+50}{2*4}=\frac{60}{8}
=7+1/2
$