(162x^2-171x-108)=0

Solution for (162x^2-171x-108)=0 equation:

(162x^2-171x-108)=0

We get rid of parentheses

162x^2-171x-108=0

a = 162; b = -171; c = -108;
Δ = b2-4ac
Δ = -1712-4·162·(-108)
Δ = 99225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{99225}=315$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-171)-315}{2*162}=\frac{-144}{324}
=-4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-171)+315}{2*162}=\frac{486}{324}
=1+1/2
$