18x^2-27x^2+13x-2=0

Solution for 18x^2-27x^2+13x-2=0 equation:

18x^2-27x^2+13x-2=0

We add all the numbers together, and all the variables

-9x^2+13x-2=0

a = -9; b = 13; c = -2;
Δ = b2-4ac
Δ = 132-4·(-9)·(-2)
Δ = 97
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{-(13)-\sqrt{97}}{2*-9}=\frac{-13-\sqrt{97}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{97}}{2*-9}=\frac{-13+\sqrt{97}}{-18}
$