4(x-7)=3(91/3x)

Solution for 4(x-7)=3(91/3x) equation:

4(x-7)=3(91/3x)

We move all terms to the left:

4(x-7)-(3(91/3x))=0


Domain of the equation: 3x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(x-7)-(3(+91/3x))=0

We multiply parentheses

4x-(3(+91/3x))-28=0

We multiply all the terms by the denominator


4x*3x))-(3(-28*3x))+91=0

Wy multiply elements

12x^2-84x=0

a = 12; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·12·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*12}=\frac{168}{24}
=7
$