1/4x-12.25=9x

Solution for 1/4x-12.25=9x equation:

1/4x-12.25=9x

We move all terms to the left:

1/4x-12.25-(9x)=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-12.25=0

We multiply all the terms by the denominator


-9x*4x-(12.25)*4x+1=0

We multiply parentheses

-9x*4x-49x+1=0

Wy multiply elements

-36x^2-49x+1=0

a = -36; b = -49; c = +1;
Δ = b2-4ac
Δ = -492-4·(-36)·1
Δ = 2545
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{2545}}{2*-36}=\frac{49-\sqrt{2545}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2545}}{2*-36}=\frac{49+\sqrt{2545}}{-72}
$