2x(x+5)=75x+x2

Solution for 2x(x+5)=75x+x2 equation:

2x(x+5)=75x+x2

We move all terms to the left:

2x(x+5)-(75x+x2)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-65x=0

a = 1; b = -65; c = 0;
Δ = b2-4ac
Δ = -652-4·1·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-65}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+65}{2*1}=\frac{130}{2}
=65
$