5/10x+5=4/5x-1

Solution for 5/10x+5=4/5x-1 equation:

5/10x+5=4/5x-1

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

5/10x-4/5x+1+5=0

We calculate fractions


25x/50x^2+(-40x)/50x^2+1+5=0

We add all the numbers together, and all the variables

25x/50x^2+(-40x)/50x^2+6=0

We multiply all the terms by the denominator


25x+(-40x)+6*50x^2=0

Wy multiply elements

300x^2+25x+(-40x)=0

We get rid of parentheses

300x^2+25x-40x=0

We add all the numbers together, and all the variables

300x^2-15x=0

a = 300; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·300·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*300}=\frac{0}{600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*300}=\frac{30}{600}
=1/20
$