3x(2x-10)=2(2x-12)

Solution for 3x(2x-10)=2(2x-12) equation:

3x(2x-10)=2(2x-12)

We move all terms to the left:

3x(2x-10)-(2(2x-12))=0

We multiply parentheses

6x^2-30x-(2(2x-12))=0


We calculate terms in parentheses: -(2(2x-12)), so:

2(2x-12)

We multiply parentheses

4x-24

Back to the equation:

-(4x-24)


We get rid of parentheses

6x^2-30x-4x+24=0

We add all the numbers together, and all the variables

6x^2-34x+24=0

a = 6; b = -34; c = +24;
Δ = b2-4ac
Δ = -342-4·6·24
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{145}}{2*6}=\frac{34-2\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{145}}{2*6}=\frac{34+2\sqrt{145}}{12}
$