4x+15=3x(x+4)

Solution for 4x+15=3x(x+4) equation:

4x+15=3x(x+4)

We move all terms to the left:

4x+15-(3x(x+4))=0


We calculate terms in parentheses: -(3x(x+4)), so:

3x(x+4)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

-3x^2+4x-12x+15=0

We add all the numbers together, and all the variables

-3x^2-8x+15=0

a = -3; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·(-3)·15
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{61}}{2*-3}=\frac{8-2\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{61}}{2*-3}=\frac{8+2\sqrt{61}}{-6}
$