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

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

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

We move all terms to the left:

7/5x+5-(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

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

We calculate fractions


42x/30x^2+(-25x)/30x^2+4+5=0

We add all the numbers together, and all the variables

42x/30x^2+(-25x)/30x^2+9=0

We multiply all the terms by the denominator


42x+(-25x)+9*30x^2=0

Wy multiply elements

270x^2+42x+(-25x)=0

We get rid of parentheses

270x^2+42x-25x=0

We add all the numbers together, and all the variables

270x^2+17x=0

a = 270; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·270·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*270}=\frac{-34}{540}
=-17/270
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*270}=\frac{0}{540}
=0
$