(x-6)-1/4x=45

Solution for (x-6)-1/4x=45 equation:

(x-6)-1/4x=45

We move all terms to the left:

(x-6)-1/4x-(45)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

x-1/4x-6-45=0

We multiply all the terms by the denominator


x*4x-6*4x-45*4x-1=0

Wy multiply elements

4x^2-24x-180x-1=0

We add all the numbers together, and all the variables

4x^2-204x-1=0

a = 4; b = -204; c = -1;
Δ = b2-4ac
Δ = -2042-4·4·(-1)
Δ = 41632
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:

$\sqrt{\Delta}=\sqrt{41632}=\sqrt{16*2602}=\sqrt{16}*\sqrt{2602}=4\sqrt{2602}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-4\sqrt{2602}}{2*4}=\frac{204-4\sqrt{2602}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+4\sqrt{2602}}{2*4}=\frac{204+4\sqrt{2602}}{8}
$