(9/2)(x+3)=27

Solution for (9/2)(x+3)=27 equation:

(9/2)(x+3)=27

We move all terms to the left:

(9/2)(x+3)-(27)=0


Domain of the equation: 2)(x+3)!=0

x∈R


We add all the numbers together, and all the variables

(+9/2)(x+3)-27=0

We multiply parentheses ..

(+9x^2+9/2*3)-27=0

We multiply all the terms by the denominator


(+9x^2+9-27*2*3)=0

We get rid of parentheses

9x^2+9-27*2*3=0

We add all the numbers together, and all the variables

9x^2-153=0

a = 9; b = 0; c = -153;
Δ = b2-4ac
Δ = 02-4·9·(-153)
Δ = 5508
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5508}=\sqrt{324*17}=\sqrt{324}*\sqrt{17}=18\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{17}}{2*9}=\frac{0-18\sqrt{17}}{18}
=-\frac{18\sqrt{17}}{18}
=-\sqrt{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{17}}{2*9}=\frac{0+18\sqrt{17}}{18}
=\frac{18\sqrt{17}}{18}
=\sqrt{17}
$