5/6x-10=2x+4

Solution for 5/6x-10=2x+4 equation:

5/6x-10=2x+4

We move all terms to the left:

5/6x-10-(2x+4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/6x-2x-4-10=0

We multiply all the terms by the denominator


-2x*6x-4*6x-10*6x+5=0

Wy multiply elements

-12x^2-24x-60x+5=0

We add all the numbers together, and all the variables

-12x^2-84x+5=0

a = -12; b = -84; c = +5;
Δ = b2-4ac
Δ = -842-4·(-12)·5
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-8\sqrt{114}}{2*-12}=\frac{84-8\sqrt{114}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+8\sqrt{114}}{2*-12}=\frac{84+8\sqrt{114}}{-24}
$