5x^2/2=146

Solution for 5x^2/2=146 equation:

5x^2/2=146

We move all terms to the left:

5x^2/2-(146)=0

We multiply all the terms by the denominator


5x^2-146*2=0

We add all the numbers together, and all the variables

5x^2-292=0

a = 5; b = 0; c = -292;
Δ = b2-4ac
Δ = 02-4·5·(-292)
Δ = 5840
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:

$\sqrt{\Delta}=\sqrt{5840}=\sqrt{16*365}=\sqrt{16}*\sqrt{365}=4\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{365}}{2*5}=\frac{0-4\sqrt{365}}{10}
=-\frac{4\sqrt{365}}{10}
=-\frac{2\sqrt{365}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{365}}{2*5}=\frac{0+4\sqrt{365}}{10}
=\frac{4\sqrt{365}}{10}
=\frac{2\sqrt{365}}{5}
$