9x2-65x+14x=0

Solution for 9x2-65x+14x=0 equation:

9x^2-65x+14x=0

We add all the numbers together, and all the variables

9x^2-51x=0

a = 9; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·9·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*9}=\frac{102}{18}
=5+2/3
$