s-6=(2/3)(s-3)

Solution for s-6=(2/3)(s-3) equation:

s-6=(2/3)(s-3)

We move all terms to the left:

s-6-((2/3)(s-3))=0


Domain of the equation: 3)(s-3))!=0

s∈R


We add all the numbers together, and all the variables

s-((+2/3)(s-3))-6=0

We multiply parentheses ..

-((+2s^2+2/3*-3))+s-6=0

We multiply all the terms by the denominator


-((+2s^2+2+s*3*-3))-6*3*-3))=0


We calculate terms in parentheses: -((+2s^2+2+s*3*-3)), so:

(+2s^2+2+s*3*-3)

We get rid of parentheses

2s^2+s*3*+2-3

We add all the numbers together, and all the variables

2s^2+s*3*-1

Wy multiply elements

2s^2+3s^2-1

We add all the numbers together, and all the variables

5s^2-1

Back to the equation:

-(5s^2-1)


We add all the numbers together, and all the variables

-(5s^2-1)=0

We get rid of parentheses

-5s^2+1=0

a = -5; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-5)·1
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*-5}=\frac{0-2\sqrt{5}}{-10}
=-\frac{2\sqrt{5}}{-10}
=-\frac{\sqrt{5}}{-5}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*-5}=\frac{0+2\sqrt{5}}{-10}
=\frac{2\sqrt{5}}{-10}
=\frac{\sqrt{5}}{-5}
$