0.5b^2+4b-172.5=0

Solution for 0.5b^2+4b-172.5=0 equation:

0.5b^2+4b-172.5=0

a = 0.5; b = 4; c = -172.5;
Δ = b2-4ac
Δ = 42-4·0.5·(-172.5)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-19}{2*0.5}=\frac{-23}{1}
=-23
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+19}{2*0.5}=\frac{15}{1}
=15
$