5/9s-14=7/18s-16

Solution for 5/9s-14=7/18s-16 equation:

5/9s-14=7/18s-16

We move all terms to the left:

5/9s-14-(7/18s-16)=0


Domain of the equation: 9s!=0

s!=0/9

s!=0

s∈R



Domain of the equation: 18s-16)!=0

s∈R


We get rid of parentheses

5/9s-7/18s+16-14=0

We calculate fractions


90s/162s^2+(-63s)/162s^2+16-14=0

We add all the numbers together, and all the variables

90s/162s^2+(-63s)/162s^2+2=0

We multiply all the terms by the denominator


90s+(-63s)+2*162s^2=0

Wy multiply elements

324s^2+90s+(-63s)=0

We get rid of parentheses

324s^2+90s-63s=0

We add all the numbers together, and all the variables

324s^2+27s=0

a = 324; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·324·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*324}=\frac{-54}{648}
=-1/12
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*324}=\frac{0}{648}
=0
$