7x^2-7x+21=9x^2+6x-21

Solution for 7x^2-7x+21=9x^2+6x-21 equation:

7x^2-7x+21=9x^2+6x-21

We move all terms to the left:

7x^2-7x+21-(9x^2+6x-21)=0

We get rid of parentheses

7x^2-9x^2-7x-6x+21+21=0

We add all the numbers together, and all the variables

-2x^2-13x+42=0

a = -2; b = -13; c = +42;
Δ = b2-4ac
Δ = -132-4·(-2)·42
Δ = 505
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{-(-13)-\sqrt{505}}{2*-2}=\frac{13-\sqrt{505}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{505}}{2*-2}=\frac{13+\sqrt{505}}{-4}
$