0.5x^2+10x-287.5=0

Solution for 0.5x^2+10x-287.5=0 equation:

0.5x^2+10x-287.5=0

a = 0.5; b = 10; c = -287.5;
Δ = b2-4ac
Δ = 102-4·0.5·(-287.5)
Δ = 675
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{675}=\sqrt{225*3}=\sqrt{225}*\sqrt{3}=15\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-15\sqrt{3}}{2*0.5}=\frac{-10-15\sqrt{3}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+15\sqrt{3}}{2*0.5}=\frac{-10+15\sqrt{3}}{1}
$