/7x-3=4x+9*

Solution for /7x-3=4x+9* equation:

/7x-3=4x+9*

We move all terms to the left:

/7x-3-(4x+9*)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

/7x-(+4x)-3=0

We get rid of parentheses

/7x-4x-3=0

We multiply all the terms by the denominator


-4x*7x-3*7x+=0

We add all the numbers together, and all the variables

-4x*7x-3*7x=0

Wy multiply elements

-28x^2-21x=0

a = -28; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-28)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-28}=\frac{42}{-56}
=-3/4
$