3+4x2-2+7x2=3x2+17

Solution for 3+4x2-2+7x2=3x2+17 equation:

3+4x^2-2+7x^2=3x^2+17

We move all terms to the left:

3+4x^2-2+7x^2-(3x^2+17)=0

We add all the numbers together, and all the variables

11x^2-(3x^2+17)+1=0

We get rid of parentheses

11x^2-3x^2-17+1=0

We add all the numbers together, and all the variables

8x^2-16=0

a = 8; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·8·(-16)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*8}=\frac{0-16\sqrt{2}}{16}
=-\frac{16\sqrt{2}}{16}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*8}=\frac{0+16\sqrt{2}}{16}
=\frac{16\sqrt{2}}{16}
=\sqrt{2}
$