0.5x^2+1.5x-45.5=0

Solution for 0.5x^2+1.5x-45.5=0 equation:

0.5x^2+1.5x-45.5=0

a = 0.5; b = 1.5; c = -45.5;
Δ = b2-4ac
Δ = 1.52-4·0.5·(-45.5)
Δ = 93.25
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{93.25}}{2*0.5}=\frac{-1.5-\sqrt{93.25}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{93.25}}{2*0.5}=\frac{-1.5+\sqrt{93.25}}{1}
$