5/16x-30=2/7x-27

Solution for 5/16x-30=2/7x-27 equation:

5/16x-30=2/7x-27

We move all terms to the left:

5/16x-30-(2/7x-27)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R



Domain of the equation: 7x-27)!=0

x∈R


We get rid of parentheses

5/16x-2/7x+27-30=0

We calculate fractions


35x/112x^2+(-32x)/112x^2+27-30=0

We add all the numbers together, and all the variables

35x/112x^2+(-32x)/112x^2-3=0

We multiply all the terms by the denominator


35x+(-32x)-3*112x^2=0

Wy multiply elements

-336x^2+35x+(-32x)=0

We get rid of parentheses

-336x^2+35x-32x=0

We add all the numbers together, and all the variables

-336x^2+3x=0

a = -336; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-336)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-336}=\frac{-6}{-672}
=1/112
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-336}=\frac{0}{-672}
=0
$