8x/5x+3=10-2/7x

Solution for 8x/5x+3=10-2/7x equation:

8x/5x+3=10-2/7x

We move all terms to the left:

8x/5x+3-(10-2/7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x/5x-(-2/7x+10)+3=0

We get rid of parentheses

8x/5x+2/7x-10+3=0

We calculate fractions


56x^2/35x^2+10x/35x^2-10+3=0

We add all the numbers together, and all the variables

56x^2/35x^2+10x/35x^2-7=0

We multiply all the terms by the denominator


56x^2+10x-7*35x^2=0

Wy multiply elements

56x^2-245x^2+10x=0

We add all the numbers together, and all the variables

-189x^2+10x=0

a = -189; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-189)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-189}=\frac{-20}{-378}
=10/189
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-189}=\frac{0}{-378}
=0
$