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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2-10x-(4x-3(x-6))=0


We calculate terms in parentheses: -(4x-3(x-6)), so:

4x-3(x-6)

We multiply parentheses

4x-3x+18

We add all the numbers together, and all the variables

x+18

Back to the equation:

-(x+18)


We get rid of parentheses

6x^2-10x-x-18=0

We add all the numbers together, and all the variables

6x^2-11x-18=0

a = 6; b = -11; c = -18;
Δ = b2-4ac
Δ = -112-4·6·(-18)
Δ = 553
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{553}}{2*6}=\frac{11-\sqrt{553}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{553}}{2*6}=\frac{11+\sqrt{553}}{12}
$