4/5x-5=1/2x+1

Solution for 4/5x-5=1/2x+1 equation:

4/5x-5=1/2x+1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

4/5x-1/2x-1-5=0

We calculate fractions


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

We add all the numbers together, and all the variables

8x/10x^2+(-5x)/10x^2-6=0

We multiply all the terms by the denominator


8x+(-5x)-6*10x^2=0

Wy multiply elements

-60x^2+8x+(-5x)=0

We get rid of parentheses

-60x^2+8x-5x=0

We add all the numbers together, and all the variables

-60x^2+3x=0

a = -60; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-60)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-60}=\frac{-6}{-120}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-60}=\frac{0}{-120}
=0
$