12/5x=x+35

Solution for 12/5x=x+35 equation:

12/5x=x+35

We move all terms to the left:

12/5x-(x+35)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

12/5x-x-35=0

We multiply all the terms by the denominator


-x*5x-35*5x+12=0

Wy multiply elements

-5x^2-175x+12=0

a = -5; b = -175; c = +12;
Δ = b2-4ac
Δ = -1752-4·(-5)·12
Δ = 30865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-175)-\sqrt{30865}}{2*-5}=\frac{175-\sqrt{30865}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+\sqrt{30865}}{2*-5}=\frac{175+\sqrt{30865}}{-10}
$