10x^2=11

Solution for 10x^2=11 equation:

10x^2=11

We move all terms to the left:

10x^2-(11)=0

a = 10; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·10·(-11)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*10}=\frac{0-2\sqrt{110}}{20}
=-\frac{2\sqrt{110}}{20}
=-\frac{\sqrt{110}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*10}=\frac{0+2\sqrt{110}}{20}
=\frac{2\sqrt{110}}{20}
=\frac{\sqrt{110}}{10}
$