7f^2-9=8f

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

7f^2-9=8f

We move all terms to the left:

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

a = 7; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·7·(-9)
Δ = 316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{79}}{2*7}=\frac{8-2\sqrt{79}}{14}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{79}}{2*7}=\frac{8+2\sqrt{79}}{14}
$