5/6x+3=12x-9

Solution for 5/6x+3=12x-9 equation:

5/6x+3=12x-9

We move all terms to the left:

5/6x+3-(12x-9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/6x-12x+9+3=0

We multiply all the terms by the denominator


-12x*6x+9*6x+3*6x+5=0

Wy multiply elements

-72x^2+54x+18x+5=0

We add all the numbers together, and all the variables

-72x^2+72x+5=0

a = -72; b = 72; c = +5;
Δ = b2-4ac
Δ = 722-4·(-72)·5
Δ = 6624
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:

$\sqrt{\Delta}=\sqrt{6624}=\sqrt{144*46}=\sqrt{144}*\sqrt{46}=12\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{46}}{2*-72}=\frac{-72-12\sqrt{46}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{46}}{2*-72}=\frac{-72+12\sqrt{46}}{-144}
$