4x(x+3)=3(15+x^2)

Solution for 4x(x+3)=3(15+x^2) equation:

4x(x+3)=3(15+x^2)

We move all terms to the left:

4x(x+3)-(3(15+x^2))=0

We multiply parentheses

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


We calculate terms in parentheses: -(3(15+x^2)), so:

3(15+x^2)

We multiply parentheses

3x^2+45

Back to the equation:

-(3x^2+45)


We add all the numbers together, and all the variables

4x^2+12x-(3x^2+45)=0

We get rid of parentheses

4x^2-3x^2+12x-45=0

We add all the numbers together, and all the variables

x^2+12x-45=0

a = 1; b = 12; c = -45;
Δ = b2-4ac
Δ = 122-4·1·(-45)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*1}=\frac{6}{2}
=3
$