7x2=777

Solution for 7x2=777 equation:

7x^2=777

We move all terms to the left:

7x^2-(777)=0

a = 7; b = 0; c = -777;
Δ = b2-4ac
Δ = 02-4·7·(-777)
Δ = 21756
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:

$\sqrt{\Delta}=\sqrt{21756}=\sqrt{196*111}=\sqrt{196}*\sqrt{111}=14\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{111}}{2*7}=\frac{0-14\sqrt{111}}{14}
=-\frac{14\sqrt{111}}{14}
=-\sqrt{111}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{111}}{2*7}=\frac{0+14\sqrt{111}}{14}
=\frac{14\sqrt{111}}{14}
=\sqrt{111}
$