X+2(1/6x+2)=6/5x+16

Solution for X+2(1/6x+2)=6/5x+16 equation:

X+2(1/6X+2)=6/5X+16

We move all terms to the left:

X+2(1/6X+2)-(6/5X+16)=0


Domain of the equation: 6X+2)!=0

X∈R



Domain of the equation: 5X+16)!=0

X∈R


We multiply parentheses

X+2X-(6/5X+16)+4=0

We get rid of parentheses

X+2X-6/5X-16+4=0

We multiply all the terms by the denominator


X*5X+2X*5X-16*5X+4*5X-6=0

Wy multiply elements

5X^2+10X^2-80X+20X-6=0

We add all the numbers together, and all the variables

15X^2-60X-6=0

a = 15; b = -60; c = -6;
Δ = b2-4ac
Δ = -602-4·15·(-6)
Δ = 3960
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:

$\sqrt{\Delta}=\sqrt{3960}=\sqrt{36*110}=\sqrt{36}*\sqrt{110}=6\sqrt{110}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{110}}{2*15}=\frac{60-6\sqrt{110}}{30}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{110}}{2*15}=\frac{60+6\sqrt{110}}{30}
$