5/6x+15=76x+9

Solution for 5/6x+15=76x+9 equation:

5/6x+15=76x+9

We move all terms to the left:

5/6x+15-(76x+9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/6x-76x-9+15=0

We multiply all the terms by the denominator


-76x*6x-9*6x+15*6x+5=0

Wy multiply elements

-456x^2-54x+90x+5=0

We add all the numbers together, and all the variables

-456x^2+36x+5=0

a = -456; b = 36; c = +5;
Δ = b2-4ac
Δ = 362-4·(-456)·5
Δ = 10416
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:

$\sqrt{\Delta}=\sqrt{10416}=\sqrt{16*651}=\sqrt{16}*\sqrt{651}=4\sqrt{651}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{651}}{2*-456}=\frac{-36-4\sqrt{651}}{-912}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{651}}{2*-456}=\frac{-36+4\sqrt{651}}{-912}
$