2x^2+6=146

Solution for 2x^2+6=146 equation:

2x^2+6=146

We move all terms to the left:

2x^2+6-(146)=0

We add all the numbers together, and all the variables

2x^2-140=0

a = 2; b = 0; c = -140;
Δ = b2-4ac
Δ = 02-4·2·(-140)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{70}}{2*2}=\frac{0-4\sqrt{70}}{4}
=-\frac{4\sqrt{70}}{4}
=-\sqrt{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{70}}{2*2}=\frac{0+4\sqrt{70}}{4}
=\frac{4\sqrt{70}}{4}
=\sqrt{70}
$