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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(x(10x+45)), so:

x(10x+45)

We multiply parentheses

10x^2+45x

Back to the equation:

-(10x^2+45x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-20x^2+30x=0

a = -20; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-20)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-20}=\frac{-60}{-40}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-20}=\frac{0}{-40}
=0
$