x2/4=5777

Solution for x2/4=5777 equation:

x2/4=5777

We move all terms to the left:

x2/4-(5777)=0

We multiply all the terms by the denominator


x2-5777*4=0

We add all the numbers together, and all the variables

x^2-23108=0

a = 1; b = 0; c = -23108;
Δ = b2-4ac
Δ = 02-4·1·(-23108)
Δ = 92432
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:

$\sqrt{\Delta}=\sqrt{92432}=\sqrt{16*5777}=\sqrt{16}*\sqrt{5777}=4\sqrt{5777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5777}}{2*1}=\frac{0-4\sqrt{5777}}{2}
=-\frac{4\sqrt{5777}}{2}
=-2\sqrt{5777}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5777}}{2*1}=\frac{0+4\sqrt{5777}}{2}
=\frac{4\sqrt{5777}}{2}
=2\sqrt{5777}
$