3x^2-45x-150=0

Solution for 3x^2-45x-150=0 equation:

3x^2-45x-150=0

a = 3; b = -45; c = -150;
Δ = b2-4ac
Δ = -452-4·3·(-150)
Δ = 3825
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:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-15\sqrt{17}}{2*3}=\frac{45-15\sqrt{17}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+15\sqrt{17}}{2*3}=\frac{45+15\sqrt{17}}{6}
$