18u^2-1=34

Solution for 18u^2-1=34 equation:

18u^2-1=34

We move all terms to the left:

18u^2-1-(34)=0

We add all the numbers together, and all the variables

18u^2-35=0

a = 18; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·18·(-35)
Δ = 2520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{70}}{2*18}=\frac{0-6\sqrt{70}}{36}
=-\frac{6\sqrt{70}}{36}
=-\frac{\sqrt{70}}{6}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{70}}{2*18}=\frac{0+6\sqrt{70}}{36}
=\frac{6\sqrt{70}}{36}
=\frac{\sqrt{70}}{6}
$