(5-5x)(6-5x)=75x^2

Solution for (5-5x)(6-5x)=75x^2 equation:

(5-5x)(6-5x)=75x^2

We move all terms to the left:

(5-5x)(6-5x)-(75x^2)=0

determiningTheFunctionDomain
-75x^2+(5-5x)(6-5x)=0

We add all the numbers together, and all the variables

-75x^2+(-5x+5)(-5x+6)=0

We multiply parentheses ..

-75x^2+(+25x^2-30x-25x+30)=0

We get rid of parentheses

-75x^2+25x^2-30x-25x+30=0

We add all the numbers together, and all the variables

-50x^2-55x+30=0

a = -50; b = -55; c = +30;
Δ = b2-4ac
Δ = -552-4·(-50)·30
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{-(-55)-95}{2*-50}=\frac{-40}{-100}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+95}{2*-50}=\frac{150}{-100}
=-1+1/2
$