9=-7x+7x^2

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

9=-7x+7x^2

We move all terms to the left:

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

We get rid of parentheses

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

a = -7; b = 7; c = +9;
Δ = b2-4ac
Δ = 72-4·(-7)·9
Δ = 301
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{-(7)-\sqrt{301}}{2*-7}=\frac{-7-\sqrt{301}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{301}}{2*-7}=\frac{-7+\sqrt{301}}{-14}
$