3(5x-20)=15x(x-20)

Solution for 3(5x-20)=15x(x-20) equation:

3(5x-20)=15x(x-20)

We move all terms to the left:

3(5x-20)-(15x(x-20))=0

We multiply parentheses

15x-(15x(x-20))-60=0


We calculate terms in parentheses: -(15x(x-20)), so:

15x(x-20)

We multiply parentheses

15x^2-300x

Back to the equation:

-(15x^2-300x)


We get rid of parentheses

-15x^2+15x+300x-60=0

We add all the numbers together, and all the variables

-15x^2+315x-60=0

a = -15; b = 315; c = -60;
Δ = b2-4ac
Δ = 3152-4·(-15)·(-60)
Δ = 95625
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:

$\sqrt{\Delta}=\sqrt{95625}=\sqrt{5625*17}=\sqrt{5625}*\sqrt{17}=75\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-75\sqrt{17}}{2*-15}=\frac{-315-75\sqrt{17}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+75\sqrt{17}}{2*-15}=\frac{-315+75\sqrt{17}}{-30}
$