6(x2-4)+8-2x2=7

Solution for 6(x2-4)+8-2x2=7 equation:

6(x2-4)+8-2x^2=7

We move all terms to the left:

6(x2-4)+8-2x^2-(7)=0

We add all the numbers together, and all the variables

-2x^2+6(+x^2-4)+8-7=0

We add all the numbers together, and all the variables

-2x^2+6(+x^2-4)+1=0

We multiply parentheses

-2x^2+6x^2-24+1=0

We add all the numbers together, and all the variables

4x^2-23=0

a = 4; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·4·(-23)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{23}}{2*4}=\frac{0-4\sqrt{23}}{8}
=-\frac{4\sqrt{23}}{8}
=-\frac{\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{23}}{2*4}=\frac{0+4\sqrt{23}}{8}
=\frac{4\sqrt{23}}{8}
=\frac{\sqrt{23}}{2}
$