x^2/77=4

Solution for x^2/77=4 equation:

x^2/77=4

We move all terms to the left:

x^2/77-(4)=0

We multiply all the terms by the denominator


x^2-4*77=0

We add all the numbers together, and all the variables

x^2-308=0

a = 1; b = 0; c = -308;
Δ = b2-4ac
Δ = 02-4·1·(-308)
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{77}}{2*1}=\frac{0-4\sqrt{77}}{2}
=-\frac{4\sqrt{77}}{2}
=-2\sqrt{77}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{77}}{2*1}=\frac{0+4\sqrt{77}}{2}
=\frac{4\sqrt{77}}{2}
=2\sqrt{77}
$