-1.5x^2-2.5x+75=50

Solution for -1.5x^2-2.5x+75=50 equation:

-1.5x^2-2.5x+75=50

We move all terms to the left:

-1.5x^2-2.5x+75-(50)=0

We add all the numbers together, and all the variables

-1.5x^2-2.5x+25=0

a = -1.5; b = -2.5; c = +25;
Δ = b2-4ac
Δ = -2.52-4·(-1.5)·25
Δ = 156.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.5)-\sqrt{156.25}}{2*-1.5}=\frac{2.5-\sqrt{156.25}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{156.25}}{2*-1.5}=\frac{2.5+\sqrt{156.25}}{-3}
$