8/13x+48=x

Solution for 8/13x+48=x equation:

8/13x+48=x

We move all terms to the left:

8/13x+48-(x)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8/13x+48=0

We multiply all the terms by the denominator


-1x*13x+48*13x+8=0

Wy multiply elements

-13x^2+624x+8=0

a = -13; b = 624; c = +8;
Δ = b2-4ac
Δ = 6242-4·(-13)·8
Δ = 389792
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:

$\sqrt{\Delta}=\sqrt{389792}=\sqrt{16*24362}=\sqrt{16}*\sqrt{24362}=4\sqrt{24362}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(624)-4\sqrt{24362}}{2*-13}=\frac{-624-4\sqrt{24362}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(624)+4\sqrt{24362}}{2*-13}=\frac{-624+4\sqrt{24362}}{-26}
$