2x(x+5)=75+x

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

2x(x+5)=75+x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+9x-75=0

a = 2; b = 9; c = -75;
Δ = b2-4ac
Δ = 92-4·2·(-75)
Δ = 681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{681}}{2*2}=\frac{-9-\sqrt{681}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{681}}{2*2}=\frac{-9+\sqrt{681}}{4}
$