45s^2+30s-54=0

Solution for 45s^2+30s-54=0 equation:

45s^2+30s-54=0

a = 45; b = 30; c = -54;
Δ = b2-4ac
Δ = 302-4·45·(-54)
Δ = 10620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10620}=\sqrt{36*295}=\sqrt{36}*\sqrt{295}=6\sqrt{295}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{295}}{2*45}=\frac{-30-6\sqrt{295}}{90}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{295}}{2*45}=\frac{-30+6\sqrt{295}}{90}
$