-7+3/5x=4-5/6x

Solution for -7+3/5x=4-5/6x equation:

-7+3/5x=4-5/6x

We move all terms to the left:

-7+3/5x-(4-5/6x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(-5/6x+4)-7=0

We get rid of parentheses

3/5x+5/6x-4-7=0

We calculate fractions


18x/30x^2+25x/30x^2-4-7=0

We add all the numbers together, and all the variables

18x/30x^2+25x/30x^2-11=0

We multiply all the terms by the denominator


18x+25x-11*30x^2=0

We add all the numbers together, and all the variables

43x-11*30x^2=0

Wy multiply elements

-330x^2+43x=0

a = -330; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-330)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-330}=\frac{-86}{-660}
=43/330
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-330}=\frac{0}{-660}
=0
$