4x2-7=4(2-2)+1

Solution for 4x2-7=4(2-2)+1 equation:

4x^2-7=4(2-2)+1

We move all terms to the left:

4x^2-7-(4(2-2)+1)=0

We add all the numbers together, and all the variables

4x^2-7-(40+1)=0

We add all the numbers together, and all the variables

4x^2-48=0

a = 4; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·4·(-48)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*4}=\frac{0-16\sqrt{3}}{8}
=-\frac{16\sqrt{3}}{8}
=-2\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*4}=\frac{0+16\sqrt{3}}{8}
=\frac{16\sqrt{3}}{8}
=2\sqrt{3}
$