-2x=1/4x-9

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

-2x=1/4x-9

We move all terms to the left:

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


Domain of the equation: 4x-9)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -8; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-8)·(-1)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{79}}{2*-8}=\frac{-36-4\sqrt{79}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{79}}{2*-8}=\frac{-36+4\sqrt{79}}{-16}
$