6x^2=x^2+7-x

Solution for 6x^2=x^2+7-x equation:

6x^2=x^2+7-x

We move all terms to the left:

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

We get rid of parentheses

6x^2-x^2+x-7=0

We add all the numbers together, and all the variables

5x^2+x-7=0

a = 5; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·5·(-7)
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{141}}{2*5}=\frac{-1-\sqrt{141}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{141}}{2*5}=\frac{-1+\sqrt{141}}{10}
$