0.5(x^2)=980

Solution for 0.5(x^2)=980 equation:

0.5(x^2)=980

We move all terms to the left:

0.5(x^2)-(980)=0

a = 0.5; b = 0; c = -980;
Δ = b2-4ac
Δ = 02-4·0.5·(-980)
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{10}}{2*0.5}=\frac{0-14\sqrt{10}}{1}
=-\frac{14\sqrt{10}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{10}}{2*0.5}=\frac{0+14\sqrt{10}}{1}
=\frac{14\sqrt{10}}{1}
$