11x^2-34+3=0

Solution for 11x^2-34+3=0 equation:

11x^2-34+3=0

We add all the numbers together, and all the variables

11x^2-31=0

a = 11; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·11·(-31)
Δ = 1364
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:

$\sqrt{\Delta}=\sqrt{1364}=\sqrt{4*341}=\sqrt{4}*\sqrt{341}=2\sqrt{341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{341}}{2*11}=\frac{0-2\sqrt{341}}{22}
=-\frac{2\sqrt{341}}{22}
=-\frac{\sqrt{341}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{341}}{2*11}=\frac{0+2\sqrt{341}}{22}
=\frac{2\sqrt{341}}{22}
=\frac{\sqrt{341}}{11}
$