b^2-1.5b-52=0

Solution for b^2-1.5b-52=0 equation:

b^2-1.5b-52=0

a = 1; b = -1.5; c = -52;
Δ = b2-4ac
Δ = -1.52-4·1·(-52)
Δ = 210.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{210.25}}{2*1}=\frac{1.5-\sqrt{210.25}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{210.25}}{2*1}=\frac{1.5+\sqrt{210.25}}{2}
$