87/10x=6-1/5x

Solution for 87/10x=6-1/5x equation:

87/10x=6-1/5x

We move all terms to the left:

87/10x-(6-1/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

87/10x-(-1/5x+6)=0

We get rid of parentheses

87/10x+1/5x-6=0

We calculate fractions


435x/50x^2+10x/50x^2-6=0

We multiply all the terms by the denominator


435x+10x-6*50x^2=0

We add all the numbers together, and all the variables

445x-6*50x^2=0

Wy multiply elements

-300x^2+445x=0

a = -300; b = 445; c = 0;
Δ = b2-4ac
Δ = 4452-4·(-300)·0
Δ = 198025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{198025}=445$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(445)-445}{2*-300}=\frac{-890}{-600}
=1+29/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(445)+445}{2*-300}=\frac{0}{-600}
=0
$