5(0.5x-4)=5/2x-20

Solution for 5(0.5x-4)=5/2x-20 equation:

5(0.5x-4)=5/2x-20

We move all terms to the left:

5(0.5x-4)-(5/2x-20)=0


Domain of the equation: 2x-20)!=0

x∈R


We multiply parentheses

0x-(5/2x-20)-20=0

We get rid of parentheses

0x-5/2x+20-20=0

We multiply all the terms by the denominator


0x*2x+20*2x-20*2x-5=0

Wy multiply elements

0x^2+40x-40x-5=0

We add all the numbers together, and all the variables

x^2-5=0

a = 1; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·1·(-5)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*1}=\frac{0-2\sqrt{5}}{2}
=-\frac{2\sqrt{5}}{2}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*1}=\frac{0+2\sqrt{5}}{2}
=\frac{2\sqrt{5}}{2}
=\sqrt{5}
$