13/21x=x-16

Solution for 13/21x=x-16 equation:

13/21x=x-16

We move all terms to the left:

13/21x-(x-16)=0


Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We get rid of parentheses

13/21x-x+16=0

We multiply all the terms by the denominator


-x*21x+16*21x+13=0

Wy multiply elements

-21x^2+336x+13=0

a = -21; b = 336; c = +13;
Δ = b2-4ac
Δ = 3362-4·(-21)·13
Δ = 113988
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{113988}=\sqrt{4*28497}=\sqrt{4}*\sqrt{28497}=2\sqrt{28497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(336)-2\sqrt{28497}}{2*-21}=\frac{-336-2\sqrt{28497}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+2\sqrt{28497}}{2*-21}=\frac{-336+2\sqrt{28497}}{-42}
$