-1.5x^2+34x-100=0

Solution for -1.5x^2+34x-100=0 equation:

-1.5x^2+34x-100=0

a = -1.5; b = 34; c = -100;
Δ = b2-4ac
Δ = 342-4·(-1.5)·(-100)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{139}}{2*-1.5}=\frac{-34-2\sqrt{139}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{139}}{2*-1.5}=\frac{-34+2\sqrt{139}}{-3}
$