9x(2x-3)=26

Solution for 9x(2x-3)=26 equation:

9x(2x-3)=26

We move all terms to the left:

9x(2x-3)-(26)=0

We multiply parentheses

18x^2-27x-26=0

a = 18; b = -27; c = -26;
Δ = b2-4ac
Δ = -272-4·18·(-26)
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{-(-27)-51}{2*18}=\frac{-24}{36}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+51}{2*18}=\frac{78}{36}
=2+1/6
$