4/5x+1=5/6x-4

Solution for 4/5x+1=5/6x-4 equation:

4/5x+1=5/6x-4

We move all terms to the left:

4/5x+1-(5/6x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

4/5x-5/6x+4+1=0

We calculate fractions


24x/30x^2+(-25x)/30x^2+4+1=0

We add all the numbers together, and all the variables

24x/30x^2+(-25x)/30x^2+5=0

We multiply all the terms by the denominator


24x+(-25x)+5*30x^2=0

Wy multiply elements

150x^2+24x+(-25x)=0

We get rid of parentheses

150x^2+24x-25x=0

We add all the numbers together, and all the variables

150x^2-1x=0

a = 150; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·150·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*150}=\frac{2}{300}
=1/150
$