(2/5)(x+3)=6

Solution for (2/5)(x+3)=6 equation:

(2/5)(x+3)=6

We move all terms to the left:

(2/5)(x+3)-(6)=0


Domain of the equation: 5)(x+3)!=0

x∈R


We add all the numbers together, and all the variables

(+2/5)(x+3)-6=0

We multiply parentheses ..

(+2x^2+2/5*3)-6=0

We multiply all the terms by the denominator


(+2x^2+2-6*5*3)=0

We get rid of parentheses

2x^2+2-6*5*3=0

We add all the numbers together, and all the variables

2x^2-88=0

a = 2; b = 0; c = -88;
Δ = b2-4ac
Δ = 02-4·2·(-88)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*2}=\frac{0-8\sqrt{11}}{4}
=-\frac{8\sqrt{11}}{4}
=-2\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*2}=\frac{0+8\sqrt{11}}{4}
=\frac{8\sqrt{11}}{4}
=2\sqrt{11}
$