(7/2)x-2=4+4x

Solution for (7/2)x-2=4+4x equation:

(7/2)x-2=4+4x

We move all terms to the left:

(7/2)x-2-(4+4x)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+7/2)x-(4x+4)-2=0

We multiply parentheses

7x^2-(4x+4)-2=0

We get rid of parentheses

7x^2-4x-4-2=0

We add all the numbers together, and all the variables

7x^2-4x-6=0

a = 7; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·7·(-6)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*7}=\frac{4-2\sqrt{46}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*7}=\frac{4+2\sqrt{46}}{14}
$