7x^2=1089

Solution for 7x^2=1089 equation:

7x^2=1089

We move all terms to the left:

7x^2-(1089)=0

a = 7; b = 0; c = -1089;
Δ = b2-4ac
Δ = 02-4·7·(-1089)
Δ = 30492
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:

$\sqrt{\Delta}=\sqrt{30492}=\sqrt{4356*7}=\sqrt{4356}*\sqrt{7}=66\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-66\sqrt{7}}{2*7}=\frac{0-66\sqrt{7}}{14}
=-\frac{66\sqrt{7}}{14}
=-\frac{33\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+66\sqrt{7}}{2*7}=\frac{0+66\sqrt{7}}{14}
=\frac{66\sqrt{7}}{14}
=\frac{33\sqrt{7}}{7}
$