27x^2+100x-150=0

Solution for 27x^2+100x-150=0 equation:

27x^2+100x-150=0

a = 27; b = 100; c = -150;
Δ = b2-4ac
Δ = 1002-4·27·(-150)
Δ = 26200
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:

$\sqrt{\Delta}=\sqrt{26200}=\sqrt{100*262}=\sqrt{100}*\sqrt{262}=10\sqrt{262}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{262}}{2*27}=\frac{-100-10\sqrt{262}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{262}}{2*27}=\frac{-100+10\sqrt{262}}{54}
$