11x^2=11078

Solution for 11x^2=11078 equation:

11x^2=11078

We move all terms to the left:

11x^2-(11078)=0

a = 11; b = 0; c = -11078;
Δ = b2-4ac
Δ = 02-4·11·(-11078)
Δ = 487432
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:

$\sqrt{\Delta}=\sqrt{487432}=\sqrt{4*121858}=\sqrt{4}*\sqrt{121858}=2\sqrt{121858}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{121858}}{2*11}=\frac{0-2\sqrt{121858}}{22}
=-\frac{2\sqrt{121858}}{22}
=-\frac{\sqrt{121858}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{121858}}{2*11}=\frac{0+2\sqrt{121858}}{22}
=\frac{2\sqrt{121858}}{22}
=\frac{\sqrt{121858}}{11}
$