x/7x-4=3x+16

Solution for x/7x-4=3x+16 equation:

X/7X-4=3X+16

We move all terms to the left:

X/7X-4-(3X+16)=0


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We get rid of parentheses

X/7X-3X-16-4=0

We multiply all the terms by the denominator


X-3X*7X-16*7X-4*7X=0

Wy multiply elements

-21X^2+X-112X-28X=0

We add all the numbers together, and all the variables

-21X^2-139X=0

a = -21; b = -139; c = 0;
Δ = b2-4ac
Δ = -1392-4·(-21)·0
Δ = 19321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19321}=139$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-139)-139}{2*-21}=\frac{0}{-42}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-139)+139}{2*-21}=\frac{278}{-42}
=-6+13/21
$