5x-75=2x(x+15)

Solution for 5x-75=2x(x+15) equation:

5x-75=2x(x+15)

We move all terms to the left:

5x-75-(2x(x+15))=0


We calculate terms in parentheses: -(2x(x+15)), so:

2x(x+15)

We multiply parentheses

2x^2+30x

Back to the equation:

-(2x^2+30x)


We get rid of parentheses

-2x^2+5x-30x-75=0

We add all the numbers together, and all the variables

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

a = -2; b = -25; c = -75;
Δ = b2-4ac
Δ = -252-4·(-2)·(-75)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5}{2*-2}=\frac{20}{-4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5}{2*-2}=\frac{30}{-4}
=-7+1/2
$