22x^2+11=110

Solution for 22x^2+11=110 equation:

22x^2+11=110

We move all terms to the left:

22x^2+11-(110)=0

We add all the numbers together, and all the variables

22x^2-99=0

a = 22; b = 0; c = -99;
Δ = b2-4ac
Δ = 02-4·22·(-99)
Δ = 8712
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:

$\sqrt{\Delta}=\sqrt{8712}=\sqrt{4356*2}=\sqrt{4356}*\sqrt{2}=66\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-66\sqrt{2}}{2*22}=\frac{0-66\sqrt{2}}{44}
=-\frac{66\sqrt{2}}{44}
=-\frac{3\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+66\sqrt{2}}{2*22}=\frac{0+66\sqrt{2}}{44}
=\frac{66\sqrt{2}}{44}
=\frac{3\sqrt{2}}{2}
$