4(3x-6)=2x(5x-15)

Solution for 4(3x-6)=2x(5x-15) equation:

4(3x-6)=2x(5x-15)

We move all terms to the left:

4(3x-6)-(2x(5x-15))=0

We multiply parentheses

12x-(2x(5x-15))-24=0


We calculate terms in parentheses: -(2x(5x-15)), so:

2x(5x-15)

We multiply parentheses

10x^2-30x

Back to the equation:

-(10x^2-30x)


We get rid of parentheses

-10x^2+12x+30x-24=0

We add all the numbers together, and all the variables

-10x^2+42x-24=0

a = -10; b = 42; c = -24;
Δ = b2-4ac
Δ = 422-4·(-10)·(-24)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{201}}{2*-10}=\frac{-42-2\sqrt{201}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{201}}{2*-10}=\frac{-42+2\sqrt{201}}{-20}
$