150-100x-12x^2=0

Solution for 150-100x-12x^2=0 equation:

150-100x-12x^2=0

a = -12; b = -100; c = +150;
Δ = b2-4ac
Δ = -1002-4·(-12)·150
Δ = 17200
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:

$\sqrt{\Delta}=\sqrt{17200}=\sqrt{400*43}=\sqrt{400}*\sqrt{43}=20\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{43}}{2*-12}=\frac{100-20\sqrt{43}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{43}}{2*-12}=\frac{100+20\sqrt{43}}{-24}
$