(3/4)(18+s)=31.50

Solution for (3/4)(18+s)=31.50 equation:

(3/4)(18+s)=31.50

We move all terms to the left:

(3/4)(18+s)-(31.50)=0


Domain of the equation: 4)(18+s)!=0

s∈R


We add all the numbers together, and all the variables

(+3/4)(s+18)-(31.5)=0

We add all the numbers together, and all the variables

(+3/4)(s+18)-31.5=0

We multiply parentheses ..

(+3s^2+3/4*18)-31.5=0

We multiply all the terms by the denominator


(+3s^2+3-(31.5)*4*18)=0


We calculate terms in parentheses: +(+3s^2+3-(31.5)*4*18), so:

+3s^2+3-(31.5)*4*18

determiningTheFunctionDomain
3s^2+3-(31.5)*4*18

We add all the numbers together, and all the variables

3s^2-2265

Back to the equation:

+(3s^2-2265)


We get rid of parentheses

3s^2-2265=0

a = 3; b = 0; c = -2265;
Δ = b2-4ac
Δ = 02-4·3·(-2265)
Δ = 27180
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:

$\sqrt{\Delta}=\sqrt{27180}=\sqrt{36*755}=\sqrt{36}*\sqrt{755}=6\sqrt{755}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{755}}{2*3}=\frac{0-6\sqrt{755}}{6}
=-\frac{6\sqrt{755}}{6}
=-\sqrt{755}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{755}}{2*3}=\frac{0+6\sqrt{755}}{6}
=\frac{6\sqrt{755}}{6}
=\sqrt{755}
$