8x(1/2x+5)=200

Solution for 8x(1/2x+5)=200 equation:

8x(1/2x+5)=200

We move all terms to the left:

8x(1/2x+5)-(200)=0


Domain of the equation: 2x+5)!=0

x∈R


We multiply parentheses

8x^2+40x-200=0

a = 8; b = 40; c = -200;
Δ = b2-4ac
Δ = 402-4·8·(-200)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{5}}{2*8}=\frac{-40-40\sqrt{5}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{5}}{2*8}=\frac{-40+40\sqrt{5}}{16}
$