10x=15(x-1/3)

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

10x=15(x-1/3)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

30x^2+x-1=0

a = 30; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·30·(-1)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*30}=\frac{-12}{60}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*30}=\frac{10}{60}
=1/6
$