(-1/3)(-2x+6)-8=-5

Solution for (-1/3)(-2x+6)-8=-5 equation:

(-1/3)(-2x+6)-8=-5

We move all terms to the left:

(-1/3)(-2x+6)-8-(-5)=0


Domain of the equation: 3)(-2x+6)!=0

x∈R


We add all the numbers together, and all the variables

(-1/3)(-2x+6)-3=0

We multiply parentheses ..

(+2x^2-1/3*6)-3=0

We multiply all the terms by the denominator


(+2x^2-1-3*3*6)=0

We get rid of parentheses

2x^2-1-3*3*6=0

We add all the numbers together, and all the variables

2x^2-55=0

a = 2; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·2·(-55)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*2}=\frac{0-2\sqrt{110}}{4}
=-\frac{2\sqrt{110}}{4}
=-\frac{\sqrt{110}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*2}=\frac{0+2\sqrt{110}}{4}
=\frac{2\sqrt{110}}{4}
=\frac{\sqrt{110}}{2}
$