1/4x-9x=105

Solution for 1/4x-9x=105 equation:

1/4x-9x=105

We move all terms to the left:

1/4x-9x-(105)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+1/4x-105=0

We multiply all the terms by the denominator


-9x*4x-105*4x+1=0

Wy multiply elements

-36x^2-420x+1=0

a = -36; b = -420; c = +1;
Δ = b2-4ac
Δ = -4202-4·(-36)·1
Δ = 176544
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:

$\sqrt{\Delta}=\sqrt{176544}=\sqrt{144*1226}=\sqrt{144}*\sqrt{1226}=12\sqrt{1226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-12\sqrt{1226}}{2*-36}=\frac{420-12\sqrt{1226}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+12\sqrt{1226}}{2*-36}=\frac{420+12\sqrt{1226}}{-72}
$