5x^2-14=9x

Solution for 5x^2-14=9x equation:

5x^2-14=9x

We move all terms to the left:

5x^2-14-(9x)=0

a = 5; b = -9; c = -14;
Δ = b2-4ac
Δ = -92-4·5·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-19}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+19}{2*5}=\frac{28}{10}
=2+4/5
$