34-18x^2=5

Solution for 34-18x^2=5 equation:

34-18x^2=5

We move all terms to the left:

34-18x^2-(5)=0

We add all the numbers together, and all the variables

-18x^2+29=0

a = -18; b = 0; c = +29;
Δ = b2-4ac
Δ = 02-4·(-18)·29
Δ = 2088
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:

$\sqrt{\Delta}=\sqrt{2088}=\sqrt{36*58}=\sqrt{36}*\sqrt{58}=6\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{58}}{2*-18}=\frac{0-6\sqrt{58}}{-36}
=-\frac{6\sqrt{58}}{-36}
=-\frac{\sqrt{58}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{58}}{2*-18}=\frac{0+6\sqrt{58}}{-36}
=\frac{6\sqrt{58}}{-36}
=\frac{\sqrt{58}}{-6}
$