2(x^2-4)+7=154

Solution for 2(x^2-4)+7=154 equation:

2(x^2-4)+7=154

We move all terms to the left:

2(x^2-4)+7-(154)=0

We add all the numbers together, and all the variables

2(x^2-4)-147=0

We multiply parentheses

2x^2-8-147=0

We add all the numbers together, and all the variables

2x^2-155=0

a = 2; b = 0; c = -155;
Δ = b2-4ac
Δ = 02-4·2·(-155)
Δ = 1240
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:

$\sqrt{\Delta}=\sqrt{1240}=\sqrt{4*310}=\sqrt{4}*\sqrt{310}=2\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{310}}{2*2}=\frac{0-2\sqrt{310}}{4}
=-\frac{2\sqrt{310}}{4}
=-\frac{\sqrt{310}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{310}}{2*2}=\frac{0+2\sqrt{310}}{4}
=\frac{2\sqrt{310}}{4}
=\frac{\sqrt{310}}{2}
$