31.5-1.2x-0.06x^2=0

Solution for 31.5-1.2x-0.06x^2=0 equation:

31.5-1.2x-0.06x^2=0

a = -0.06; b = -1.2; c = +31.5;
Δ = b2-4ac
Δ = -1.22-4·(-0.06)·31.5
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.2)-3}{2*-0.06}=\frac{-1.8}{-0.12}
=15+2.22044604925E-16/0.12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.2)+3}{2*-0.06}=\frac{4.2}{-0.12}
=-35
$