(3/4)(6x+9)=14

Solution for (3/4)(6x+9)=14 equation:

(3/4)(6x+9)=14

We move all terms to the left:

(3/4)(6x+9)-(14)=0


Domain of the equation: 4)(6x+9)!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)(6x+9)-14=0

We multiply parentheses ..

(+18x^2+3/4*9)-14=0

We multiply all the terms by the denominator


(+18x^2+3-14*4*9)=0

We get rid of parentheses

18x^2+3-14*4*9=0

We add all the numbers together, and all the variables

18x^2-501=0

a = 18; b = 0; c = -501;
Δ = b2-4ac
Δ = 02-4·18·(-501)
Δ = 36072
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:

$\sqrt{\Delta}=\sqrt{36072}=\sqrt{36*1002}=\sqrt{36}*\sqrt{1002}=6\sqrt{1002}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1002}}{2*18}=\frac{0-6\sqrt{1002}}{36}
=-\frac{6\sqrt{1002}}{36}
=-\frac{\sqrt{1002}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1002}}{2*18}=\frac{0+6\sqrt{1002}}{36}
=\frac{6\sqrt{1002}}{36}
=\frac{\sqrt{1002}}{6}
$