/7x-9=4x+22

Solution for /7x-9=4x+22 equation:

/7x-9=4x+22

We move all terms to the left:

/7x-9-(4x+22)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

/7x-4x-22-9=0

We multiply all the terms by the denominator


-4x*7x-22*7x-9*7x+=0

We add all the numbers together, and all the variables

-4x*7x-22*7x-9*7x=0

Wy multiply elements

-28x^2-154x-63x=0

We add all the numbers together, and all the variables

-28x^2-217x=0

a = -28; b = -217; c = 0;
Δ = b2-4ac
Δ = -2172-4·(-28)·0
Δ = 47089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{47089}=217$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-217)-217}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-217)+217}{2*-28}=\frac{434}{-56}
=-7+3/4
$