7x^2=2-2x

Solution for 7x^2=2-2x equation:

7x^2=2-2x

We move all terms to the left:

7x^2-(2-2x)=0

We add all the numbers together, and all the variables

7x^2-(-2x+2)=0

We get rid of parentheses

7x^2+2x-2=0

a = 7; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·7·(-2)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{15}}{2*7}=\frac{-2-2\sqrt{15}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{15}}{2*7}=\frac{-2+2\sqrt{15}}{14}
$