5x(x+3)=2(5x-3)+36

Solution for 5x(x+3)=2(5x-3)+36 equation:

5x(x+3)=2(5x-3)+36

We move all terms to the left:

5x(x+3)-(2(5x-3)+36)=0

We multiply parentheses

5x^2+15x-(2(5x-3)+36)=0


We calculate terms in parentheses: -(2(5x-3)+36), so:

2(5x-3)+36

We multiply parentheses

10x-6+36

We add all the numbers together, and all the variables

10x+30

Back to the equation:

-(10x+30)


We get rid of parentheses

5x^2+15x-10x-30=0

We add all the numbers together, and all the variables

5x^2+5x-30=0

a = 5; b = 5; c = -30;
Δ = b2-4ac
Δ = 52-4·5·(-30)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*5}=\frac{20}{10}
=2
$