(6/11)(x+5)=6

Solution for (6/11)(x+5)=6 equation:

(6/11)(x+5)=6

We move all terms to the left:

(6/11)(x+5)-(6)=0


Domain of the equation: 11)(x+5)!=0

x∈R


We add all the numbers together, and all the variables

(+6/11)(x+5)-6=0

We multiply parentheses ..

(+6x^2+6/11*5)-6=0

We multiply all the terms by the denominator


(+6x^2+6-6*11*5)=0

We get rid of parentheses

6x^2+6-6*11*5=0

We add all the numbers together, and all the variables

6x^2-324=0

a = 6; b = 0; c = -324;
Δ = b2-4ac
Δ = 02-4·6·(-324)
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{6}}{2*6}=\frac{0-36\sqrt{6}}{12}
=-\frac{36\sqrt{6}}{12}
=-3\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{6}}{2*6}=\frac{0+36\sqrt{6}}{12}
=\frac{36\sqrt{6}}{12}
=3\sqrt{6}
$