0.5x^2=970

Solution for 0.5x^2=970 equation:

0.5x^2=970

We move all terms to the left:

0.5x^2-(970)=0

a = 0.5; b = 0; c = -970;
Δ = b2-4ac
Δ = 02-4·0.5·(-970)
Δ = 1940
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:

$\sqrt{\Delta}=\sqrt{1940}=\sqrt{4*485}=\sqrt{4}*\sqrt{485}=2\sqrt{485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{485}}{2*0.5}=\frac{0-2\sqrt{485}}{1}
=-\frac{2\sqrt{485}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{485}}{2*0.5}=\frac{0+2\sqrt{485}}{1}
=\frac{2\sqrt{485}}{1}
$