90x^2+72x-54=0

Solution for 90x^2+72x-54=0 equation:

90x^2+72x-54=0

a = 90; b = 72; c = -54;
Δ = b2-4ac
Δ = 722-4·90·(-54)
Δ = 24624
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:

$\sqrt{\Delta}=\sqrt{24624}=\sqrt{1296*19}=\sqrt{1296}*\sqrt{19}=36\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-36\sqrt{19}}{2*90}=\frac{-72-36\sqrt{19}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+36\sqrt{19}}{2*90}=\frac{-72+36\sqrt{19}}{180}
$