(3/4)(x+6)=9

Solution for (3/4)(x+6)=9 equation:

(3/4)(x+6)=9

We move all terms to the left:

(3/4)(x+6)-(9)=0


Domain of the equation: 4)(x+6)!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)(x+6)-9=0

We multiply parentheses ..

(+3x^2+3/4*6)-9=0

We multiply all the terms by the denominator


(+3x^2+3-9*4*6)=0

We get rid of parentheses

3x^2+3-9*4*6=0

We add all the numbers together, and all the variables

3x^2-213=0

a = 3; b = 0; c = -213;
Δ = b2-4ac
Δ = 02-4·3·(-213)
Δ = 2556
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:

$\sqrt{\Delta}=\sqrt{2556}=\sqrt{36*71}=\sqrt{36}*\sqrt{71}=6\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{71}}{2*3}=\frac{0-6\sqrt{71}}{6}
=-\frac{6\sqrt{71}}{6}
=-\sqrt{71}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{71}}{2*3}=\frac{0+6\sqrt{71}}{6}
=\frac{6\sqrt{71}}{6}
=\sqrt{71}
$