8(5^2x-3)=48

Solution for 8(5^2x-3)=48 equation:

8(5^2x-3)=48

We move all terms to the left:

8(5^2x-3)-(48)=0

We multiply parentheses

40x^2-24-48=0

We add all the numbers together, and all the variables

40x^2-72=0

a = 40; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·40·(-72)
Δ = 11520
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:

$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{5}}{2*40}=\frac{0-48\sqrt{5}}{80}
=-\frac{48\sqrt{5}}{80}
=-\frac{3\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{5}}{2*40}=\frac{0+48\sqrt{5}}{80}
=\frac{48\sqrt{5}}{80}
=\frac{3\sqrt{5}}{5}
$