12x-7/5x+4=x

Solution for 12x-7/5x+4=x equation:

12x-7/5x+4=x

We move all terms to the left:

12x-7/5x+4-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

11x-7/5x+4=0

We multiply all the terms by the denominator


11x*5x+4*5x-7=0

Wy multiply elements

55x^2+20x-7=0

a = 55; b = 20; c = -7;
Δ = b2-4ac
Δ = 202-4·55·(-7)
Δ = 1940
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:

$\sqrt{\Delta}=\sqrt{1940}=\sqrt{4*485}=\sqrt{4}*\sqrt{485}=2\sqrt{485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{485}}{2*55}=\frac{-20-2\sqrt{485}}{110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{485}}{2*55}=\frac{-20+2\sqrt{485}}{110}
$