15x+10=5x(x+1)

Solution for 15x+10=5x(x+1) equation:

15x+10=5x(x+1)

We move all terms to the left:

15x+10-(5x(x+1))=0


We calculate terms in parentheses: -(5x(x+1)), so:

5x(x+1)

We multiply parentheses

5x^2+5x

Back to the equation:

-(5x^2+5x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -5; b = 10; c = +10;
Δ = b2-4ac
Δ = 102-4·(-5)·10
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{3}}{2*-5}=\frac{-10-10\sqrt{3}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{3}}{2*-5}=\frac{-10+10\sqrt{3}}{-10}
$