x^2/4-210=20

Solution for x^2/4-210=20 equation:

x^2/4-210=20

We move all terms to the left:

x^2/4-210-(20)=0

We add all the numbers together, and all the variables

x^2/4-230=0

We multiply all the terms by the denominator


x^2-230*4=0

We add all the numbers together, and all the variables

x^2-920=0

a = 1; b = 0; c = -920;
Δ = b2-4ac
Δ = 02-4·1·(-920)
Δ = 3680
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:

$\sqrt{\Delta}=\sqrt{3680}=\sqrt{16*230}=\sqrt{16}*\sqrt{230}=4\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{230}}{2*1}=\frac{0-4\sqrt{230}}{2}
=-\frac{4\sqrt{230}}{2}
=-2\sqrt{230}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{230}}{2*1}=\frac{0+4\sqrt{230}}{2}
=\frac{4\sqrt{230}}{2}
=2\sqrt{230}
$