3x(x-4)=24(x+15)=79

Solution for 3x(x-4)=24(x+15)=79 equation:

3x(x-4)=24(x+15)=79

We move all terms to the left:

3x(x-4)-(24(x+15))=0

We multiply parentheses

3x^2-12x-(24(x+15))=0


We calculate terms in parentheses: -(24(x+15)), so:

24(x+15)

We multiply parentheses

24x+360

Back to the equation:

-(24x+360)


We get rid of parentheses

3x^2-12x-24x-360=0

We add all the numbers together, and all the variables

3x^2-36x-360=0

a = 3; b = -36; c = -360;
Δ = b2-4ac
Δ = -362-4·3·(-360)
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{39}}{2*3}=\frac{36-12\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{39}}{2*3}=\frac{36+12\sqrt{39}}{6}
$