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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+14x^2-35x-10x+25)-150=0

We get rid of parentheses

14x^2-35x-10x+25-150=0

We add all the numbers together, and all the variables

14x^2-45x-125=0

a = 14; b = -45; c = -125;
Δ = b2-4ac
Δ = -452-4·14·(-125)
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-95}{2*14}=\frac{-50}{28}
=-1+11/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+95}{2*14}=\frac{140}{28}
=5
$