(x-5)(4x-5)=175

Solution for (x-5)(4x-5)=175 equation:

(x-5)(4x-5)=175

We move all terms to the left:

(x-5)(4x-5)-(175)=0

We multiply parentheses ..

(+4x^2-5x-20x+25)-175=0

We get rid of parentheses

4x^2-5x-20x+25-175=0

We add all the numbers together, and all the variables

4x^2-25x-150=0

a = 4; b = -25; c = -150;
Δ = b2-4ac
Δ = -252-4·4·(-150)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-55}{2*4}=\frac{-30}{8}
=-3+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+55}{2*4}=\frac{80}{8}
=10
$