(-1/12)(36x+34)-5x=22

Solution for (-1/12)(36x+34)-5x=22 equation:

(-1/12)(36x+34)-5x=22

We move all terms to the left:

(-1/12)(36x+34)-5x-(22)=0


Domain of the equation: 12)(36x+34)!=0

x∈R


We add all the numbers together, and all the variables

-5x+(-1/12)(36x+34)-22=0

We multiply parentheses ..

(-36x^2-1/12*34)-5x-22=0

We multiply all the terms by the denominator


(-36x^2-1-5x*12*34)-22*12*34)=0

We add all the numbers together, and all the variables

(-36x^2-1-5x*12*34)=0

We get rid of parentheses

-36x^2-5x*12*34-1=0

Wy multiply elements

-36x^2-2040x*3-1=0

Wy multiply elements

-36x^2-6120x-1=0

a = -36; b = -6120; c = -1;
Δ = b2-4ac
Δ = -61202-4·(-36)·(-1)
Δ = 37454256
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:

$\sqrt{\Delta}=\sqrt{37454256}=\sqrt{144*260099}=\sqrt{144}*\sqrt{260099}=12\sqrt{260099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6120)-12\sqrt{260099}}{2*-36}=\frac{6120-12\sqrt{260099}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6120)+12\sqrt{260099}}{2*-36}=\frac{6120+12\sqrt{260099}}{-72}
$