18x^2-25x-150=0

Solution for 18x^2-25x-150=0 equation:

18x^2-25x-150=0

a = 18; b = -25; c = -150;
Δ = b2-4ac
Δ = -252-4·18·(-150)
Δ = 11425
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:

$\sqrt{\Delta}=\sqrt{11425}=\sqrt{25*457}=\sqrt{25}*\sqrt{457}=5\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{457}}{2*18}=\frac{25-5\sqrt{457}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{457}}{2*18}=\frac{25+5\sqrt{457}}{36}
$