(1/2)(6x-4)+4x=26

Solution for (1/2)(6x-4)+4x=26 equation:

(1/2)(6x-4)+4x=26

We move all terms to the left:

(1/2)(6x-4)+4x-(26)=0


Domain of the equation: 2)(6x-4)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(6x-4)+4x-26=0

We add all the numbers together, and all the variables

4x+(+1/2)(6x-4)-26=0

We multiply parentheses ..

(+6x^2+1/2*-4)+4x-26=0

We multiply all the terms by the denominator


(+6x^2+1+4x*2*-4)-26*2*-4)=0

We add all the numbers together, and all the variables

(+6x^2+1+4x*2*-4)=0

We get rid of parentheses

6x^2+4x*2*+1-4=0

We add all the numbers together, and all the variables

6x^2+4x*2*-3=0

Wy multiply elements

6x^2+8x^2-3=0

We add all the numbers together, and all the variables

14x^2-3=0

a = 14; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·14·(-3)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*14}=\frac{0-2\sqrt{42}}{28}
=-\frac{2\sqrt{42}}{28}
=-\frac{\sqrt{42}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*14}=\frac{0+2\sqrt{42}}{28}
=\frac{2\sqrt{42}}{28}
=\frac{\sqrt{42}}{14}
$