10/15x-3/15x=x-1

Solution for 10/15x-3/15x=x-1 equation:

10/15x-3/15x=x-1

We move all terms to the left:

10/15x-3/15x-(x-1)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We get rid of parentheses

10/15x-3/15x-x+1=0

We multiply all the terms by the denominator


-x*15x+1*15x+10-3=0

We add all the numbers together, and all the variables

-x*15x+1*15x+7=0

Wy multiply elements

-15x^2+15x+7=0

a = -15; b = 15; c = +7;
Δ = b2-4ac
Δ = 152-4·(-15)·7
Δ = 645
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{645}}{2*-15}=\frac{-15-\sqrt{645}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{645}}{2*-15}=\frac{-15+\sqrt{645}}{-30}
$