1=x^2-9x+7x^2-63+x^2+3x+7x+21

Solution for 1=x^2-9x+7x^2-63+x^2+3x+7x+21 equation:

1=x^2-9x+7x^2-63+x^2+3x+7x+21

We move all terms to the left:

1-(x^2-9x+7x^2-63+x^2+3x+7x+21)=0

We get rid of parentheses

-x^2-7x^2-x^2+9x-3x-7x+63-21+1=0

We add all the numbers together, and all the variables

-9x^2-1x+43=0

a = -9; b = -1; c = +43;
Δ = b2-4ac
Δ = -12-4·(-9)·43
Δ = 1549
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{1549}}{2*-9}=\frac{1-\sqrt{1549}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1549}}{2*-9}=\frac{1+\sqrt{1549}}{-18}
$