5(2x+8)x=3

Solution for 5(2x+8)x=3 equation:

5(2x+8)x=3

We move all terms to the left:

5(2x+8)x-(3)=0

We multiply parentheses

10x^2+40x-3=0

a = 10; b = 40; c = -3;
Δ = b2-4ac
Δ = 402-4·10·(-3)
Δ = 1720
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:

$\sqrt{\Delta}=\sqrt{1720}=\sqrt{4*430}=\sqrt{4}*\sqrt{430}=2\sqrt{430}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{430}}{2*10}=\frac{-40-2\sqrt{430}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{430}}{2*10}=\frac{-40+2\sqrt{430}}{20}
$