1/4x-72=2x-9

Solution for 1/4x-72=2x-9 equation:

1/4x-72=2x-9

We move all terms to the left:

1/4x-72-(2x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-2x+9-72=0

We multiply all the terms by the denominator


-2x*4x+9*4x-72*4x+1=0

Wy multiply elements

-8x^2+36x-288x+1=0

We add all the numbers together, and all the variables

-8x^2-252x+1=0

a = -8; b = -252; c = +1;
Δ = b2-4ac
Δ = -2522-4·(-8)·1
Δ = 63536
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:

$\sqrt{\Delta}=\sqrt{63536}=\sqrt{5776*11}=\sqrt{5776}*\sqrt{11}=76\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-76\sqrt{11}}{2*-8}=\frac{252-76\sqrt{11}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+76\sqrt{11}}{2*-8}=\frac{252+76\sqrt{11}}{-16}
$