4(x^2-3)+3=16

Solution for 4(x^2-3)+3=16 equation:

4(x^2-3)+3=16

We move all terms to the left:

4(x^2-3)+3-(16)=0

We add all the numbers together, and all the variables

4(x^2-3)-13=0

We multiply parentheses

4x^2-12-13=0

We add all the numbers together, and all the variables

4x^2-25=0

a = 4; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·4·(-25)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*4}=\frac{20}{8}
=2+1/2
$