2(x-5)=-6x+2(x^2-10)

Solution for 2(x-5)=-6x+2(x^2-10) equation:

2(x-5)=-6x+2(x^2-10)

We move all terms to the left:

2(x-5)-(-6x+2(x^2-10))=0

We multiply parentheses

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


We calculate terms in parentheses: -(-6x+2(x^2-10)), so:

-6x+2(x^2-10)

We multiply parentheses

2x^2-6x-20

Back to the equation:

-(2x^2-6x-20)


We get rid of parentheses

-2x^2+2x+6x+20-10=0

We add all the numbers together, and all the variables

-2x^2+8x+10=0

a = -2; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-2)·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*-2}=\frac{4}{-4}
=-1
$