(4x-5)(x-5)=45x

Solution for (4x-5)(x-5)=45x equation:

(4x-5)(x-5)=45x

We move all terms to the left:

(4x-5)(x-5)-(45x)=0

We add all the numbers together, and all the variables

-45x+(4x-5)(x-5)=0

We multiply parentheses ..

(+4x^2-20x-5x+25)-45x=0

We get rid of parentheses

4x^2-20x-5x-45x+25=0

We add all the numbers together, and all the variables

4x^2-70x+25=0

a = 4; b = -70; c = +25;
Δ = b2-4ac
Δ = -702-4·4·25
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-30\sqrt{5}}{2*4}=\frac{70-30\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+30\sqrt{5}}{2*4}=\frac{70+30\sqrt{5}}{8}
$