/4x-9=2+7x-2

Solution for /4x-9=2+7x-2 equation:

/4x-9=2+7x-2

We move all terms to the left:

/4x-9-(2+7x-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

/4x-(+7x)-9=0

We get rid of parentheses

/4x-7x-9=0

We multiply all the terms by the denominator


-7x*4x-9*4x+=0

We add all the numbers together, and all the variables

-7x*4x-9*4x=0

Wy multiply elements

-28x^2-36x=0

a = -28; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-28)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-28}=\frac{72}{-56}
=-1+2/7
$