5x^2-7=9x

Solution for 5x^2-7=9x equation:

5x^2-7=9x

We move all terms to the left:

5x^2-7-(9x)=0

a = 5; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·5·(-7)
Δ = 221
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{221}}{2*5}=\frac{9-\sqrt{221}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{221}}{2*5}=\frac{9+\sqrt{221}}{10}
$