-6x(-2x+7)=(4x-2)

Solution for -6x(-2x+7)=(4x-2) equation:

-6x(-2x+7)=(4x-2)

We move all terms to the left:

-6x(-2x+7)-((4x-2))=0

We multiply parentheses

12x^2-42x-((4x-2))=0


We calculate terms in parentheses: -((4x-2)), so:

(4x-2)

We get rid of parentheses

4x-2

Back to the equation:

-(4x-2)


We get rid of parentheses

12x^2-42x-4x+2=0

We add all the numbers together, and all the variables

12x^2-46x+2=0

a = 12; b = -46; c = +2;
Δ = b2-4ac
Δ = -462-4·12·2
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{505}}{2*12}=\frac{46-2\sqrt{505}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{505}}{2*12}=\frac{46+2\sqrt{505}}{24}
$