0,5*x^2+2*x-50=0

Solution for 0,5*x^2+2*x-50=0 equation:

0.5x^2+2x-50=0

a = 0.5; b = 2; c = -50;
Δ = b2-4ac
Δ = 22-4·0.5·(-50)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{26}}{2*0.5}=\frac{-2-2\sqrt{26}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{26}}{2*0.5}=\frac{-2+2\sqrt{26}}{1}
$