x(75-10x)=45+10x

Solution for x(75-10x)=45+10x equation:

x(75-10x)=45+10x

We move all terms to the left:

x(75-10x)-(45+10x)=0

We add all the numbers together, and all the variables

x(-10x+75)-(10x+45)=0

We multiply parentheses

-10x^2+75x-(10x+45)=0

We get rid of parentheses

-10x^2+75x-10x-45=0

We add all the numbers together, and all the variables

-10x^2+65x-45=0

a = -10; b = 65; c = -45;
Δ = b2-4ac
Δ = 652-4·(-10)·(-45)
Δ = 2425
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:

$\sqrt{\Delta}=\sqrt{2425}=\sqrt{25*97}=\sqrt{25}*\sqrt{97}=5\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{97}}{2*-10}=\frac{-65-5\sqrt{97}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{97}}{2*-10}=\frac{-65+5\sqrt{97}}{-20}
$