0.5x^2+6x=32

Solution for 0.5x^2+6x=32 equation:

0.5x^2+6x=32

We move all terms to the left:

0.5x^2+6x-(32)=0

a = 0.5; b = 6; c = -32;
Δ = b2-4ac
Δ = 62-4·0.5·(-32)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*0.5}=\frac{-16}{1}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*0.5}=\frac{4}{1}
=4
$