11/15x+4=x

Solution for 11/15x+4=x equation:

11/15x+4=x

We move all terms to the left:

11/15x+4-(x)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+11/15x+4=0

We multiply all the terms by the denominator


-1x*15x+4*15x+11=0

Wy multiply elements

-15x^2+60x+11=0

a = -15; b = 60; c = +11;
Δ = b2-4ac
Δ = 602-4·(-15)·11
Δ = 4260
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:

$\sqrt{\Delta}=\sqrt{4260}=\sqrt{4*1065}=\sqrt{4}*\sqrt{1065}=2\sqrt{1065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{1065}}{2*-15}=\frac{-60-2\sqrt{1065}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{1065}}{2*-15}=\frac{-60+2\sqrt{1065}}{-30}
$