7-5/6x=-11-4x

Solution for 7-5/6x=-11-4x equation:

7-5/6x=-11-4x

We move all terms to the left:

7-5/6x-(-11-4x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-5/6x-(-4x-11)+7=0

We get rid of parentheses

-5/6x+4x+11+7=0

We multiply all the terms by the denominator


4x*6x+11*6x+7*6x-5=0

Wy multiply elements

24x^2+66x+42x-5=0

We add all the numbers together, and all the variables

24x^2+108x-5=0

a = 24; b = 108; c = -5;
Δ = b2-4ac
Δ = 1082-4·24·(-5)
Δ = 12144
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:

$\sqrt{\Delta}=\sqrt{12144}=\sqrt{16*759}=\sqrt{16}*\sqrt{759}=4\sqrt{759}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{759}}{2*24}=\frac{-108-4\sqrt{759}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{759}}{2*24}=\frac{-108+4\sqrt{759}}{48}
$