0,5x^2+25=100

Solution for 0,5x^2+25=100 equation:

0.5x^2+25=100

We move all terms to the left:

0.5x^2+25-(100)=0

We add all the numbers together, and all the variables

0.5x^2-75=0

a = 0.5; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·0.5·(-75)
Δ = 150
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:

$\sqrt{\Delta}=\sqrt{150}=\sqrt{25*6}=\sqrt{25}*\sqrt{6}=5\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{6}}{2*0.5}=\frac{0-5\sqrt{6}}{1}
=-\frac{5\sqrt{6}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{6}}{2*0.5}=\frac{0+5\sqrt{6}}{1}
=\frac{5\sqrt{6}}{1}
$