2x^2+1=25.5

Solution for 2x^2+1=25.5 equation:

2x^2+1=25.5

We move all terms to the left:

2x^2+1-(25.5)=0

We add all the numbers together, and all the variables

2x^2-24.5=0

a = 2; b = 0; c = -24.5;
Δ = b2-4ac
Δ = 02-4·2·(-24.5)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*2}=\frac{14}{4}
=3+1/2
$