y^2/20=42

Solution for y^2/20=42 equation:

y^2/20=42

We move all terms to the left:

y^2/20-(42)=0

We multiply all the terms by the denominator


y^2-42*20=0

We add all the numbers together, and all the variables

y^2-840=0

a = 1; b = 0; c = -840;
Δ = b2-4ac
Δ = 02-4·1·(-840)
Δ = 3360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*1}=\frac{0-4\sqrt{210}}{2}
=-\frac{4\sqrt{210}}{2}
=-2\sqrt{210}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*1}=\frac{0+4\sqrt{210}}{2}
=\frac{4\sqrt{210}}{2}
=2\sqrt{210}
$