7x^2-8=9x

Solution for 7x^2-8=9x equation:

7x^2-8=9x

We move all terms to the left:

7x^2-8-(9x)=0

a = 7; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·7·(-8)
Δ = 305
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{-(-9)-\sqrt{305}}{2*7}=\frac{9-\sqrt{305}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{305}}{2*7}=\frac{9+\sqrt{305}}{14}
$