4(5x2+2)=48

Solution for 4(5x2+2)=48 equation:

4(5x^2+2)=48

We move all terms to the left:

4(5x^2+2)-(48)=0

We multiply parentheses

20x^2+8-48=0

We add all the numbers together, and all the variables

20x^2-40=0

a = 20; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·20·(-40)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*20}=\frac{0-40\sqrt{2}}{40}
=-\frac{40\sqrt{2}}{40}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*20}=\frac{0+40\sqrt{2}}{40}
=\frac{40\sqrt{2}}{40}
=\sqrt{2}
$