10(3/5x)+10(4)=10(1/2x)+10(8)

Solution for 10(3/5x)+10(4)=10(1/2x)+10(8) equation:

10(3/5x)+10(4)=10(1/2x)+10(8)

We move all terms to the left:

10(3/5x)+10(4)-(10(1/2x)+10(8))=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x)+108)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10(+3/5x)-(10(+1/2x)+108)+104=0

We multiply parentheses

30x-(10(+1/2x)+108)+104=0

We multiply all the terms by the denominator


30x*2x)+108)-(10(+104*2x)+108)+1=0

Wy multiply elements

60x^2+208x=0

a = 60; b = 208; c = 0;
Δ = b2-4ac
Δ = 2082-4·60·0
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-208}{2*60}=\frac{-416}{120}
=-3+7/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+208}{2*60}=\frac{0}{120}
=0
$