2u^2-98=9

Solution for 2u^2-98=9 equation:

2u^2-98=9

We move all terms to the left:

2u^2-98-(9)=0

We add all the numbers together, and all the variables

2u^2-107=0

a = 2; b = 0; c = -107;
Δ = b2-4ac
Δ = 02-4·2·(-107)
Δ = 856
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:

$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{214}}{2*2}=\frac{0-2\sqrt{214}}{4}
=-\frac{2\sqrt{214}}{4}
=-\frac{\sqrt{214}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{214}}{2*2}=\frac{0+2\sqrt{214}}{4}
=\frac{2\sqrt{214}}{4}
=\frac{\sqrt{214}}{2}
$