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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-30x-(3(x-6))=0


We calculate terms in parentheses: -(3(x-6)), so:

3(x-6)

We multiply parentheses

3x-18

Back to the equation:

-(3x-18)


We get rid of parentheses

4x^2-30x-3x+18=0

We add all the numbers together, and all the variables

4x^2-33x+18=0

a = 4; b = -33; c = +18;
Δ = b2-4ac
Δ = -332-4·4·18
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{89}}{2*4}=\frac{33-3\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{89}}{2*4}=\frac{33+3\sqrt{89}}{8}
$