9x(2x-3)=10

Solution for 9x(2x-3)=10 equation:

9x(2x-3)=10

We move all terms to the left:

9x(2x-3)-(10)=0

We multiply parentheses

18x^2-27x-10=0

a = 18; b = -27; c = -10;
Δ = b2-4ac
Δ = -272-4·18·(-10)
Δ = 1449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{161}}{2*18}=\frac{27-3\sqrt{161}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{161}}{2*18}=\frac{27+3\sqrt{161}}{36}
$