7+2-x^2=2x-1+7x^2

Solution for 7+2-x^2=2x-1+7x^2 equation:

7+2-x^2=2x-1+7x^2

We move all terms to the left:

7+2-x^2-(2x-1+7x^2)=0

We add all the numbers together, and all the variables

-1x^2-(2x-1+7x^2)+9=0

We get rid of parentheses

-1x^2-7x^2-2x+1+9=0

We add all the numbers together, and all the variables

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

a = -8; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-8)·10
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*-8}=\frac{-16}{-16}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*-8}=\frac{20}{-16}
=-1+1/4
$