10x^2+30x-54=0

Solution for 10x^2+30x-54=0 equation:

10x^2+30x-54=0

a = 10; b = 30; c = -54;
Δ = b2-4ac
Δ = 302-4·10·(-54)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{85}}{2*10}=\frac{-30-6\sqrt{85}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{85}}{2*10}=\frac{-30+6\sqrt{85}}{20}
$