-2(x-5)=6(2-1^2x)

Solution for -2(x-5)=6(2-1^2x) equation:

-2(x-5)=6(2-1^2x)

We move all terms to the left:

-2(x-5)-(6(2-1^2x))=0

We multiply parentheses

-2x-(6(2-1^2x))+10=0


We calculate terms in parentheses: -(6(2-1^2x)), so:

6(2-1^2x)

We multiply parentheses

-6x^2+12

Back to the equation:

-(-6x^2+12)


We get rid of parentheses

6x^2-2x-12+10=0

We add all the numbers together, and all the variables

6x^2-2x-2=0

a = 6; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·6·(-2)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*6}=\frac{2-2\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*6}=\frac{2+2\sqrt{13}}{12}
$