0.5x^2-1.5x=252

Solution for 0.5x^2-1.5x=252 equation:

0.5x^2-1.5x=252

We move all terms to the left:

0.5x^2-1.5x-(252)=0

a = 0.5; b = -1.5; c = -252;
Δ = b2-4ac
Δ = -1.52-4·0.5·(-252)
Δ = 506.25
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{-(-1.5)-\sqrt{506.25}}{2*0.5}=\frac{1.5-\sqrt{506.25}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{506.25}}{2*0.5}=\frac{1.5+\sqrt{506.25}}{1}
$