x+30-4/6x=40

Solution for x+30-4/6x=40 equation:

x+30-4/6x=40

We move all terms to the left:

x+30-4/6x-(40)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

x-4/6x-10=0

We multiply all the terms by the denominator


x*6x-10*6x-4=0

Wy multiply elements

6x^2-60x-4=0

a = 6; b = -60; c = -4;
Δ = b2-4ac
Δ = -602-4·6·(-4)
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{231}}{2*6}=\frac{60-4\sqrt{231}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{231}}{2*6}=\frac{60+4\sqrt{231}}{12}
$