(1/2)(7x+2)=7x

Solution for (1/2)(7x+2)=7x equation:

(1/2)(7x+2)=7x

We move all terms to the left:

(1/2)(7x+2)-(7x)=0


Domain of the equation: 2)(7x+2)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(7x+2)-7x=0

We add all the numbers together, and all the variables

-7x+(+1/2)(7x+2)=0

We multiply parentheses ..

(+7x^2+1/2*2)-7x=0

We multiply all the terms by the denominator


(+7x^2+1-7x*2*2)=0

We get rid of parentheses

7x^2-7x*2*2+1=0

Wy multiply elements

7x^2-28x*2+1=0

Wy multiply elements

7x^2-56x+1=0

a = 7; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·7·1
Δ = 3108
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:

$\sqrt{\Delta}=\sqrt{3108}=\sqrt{4*777}=\sqrt{4}*\sqrt{777}=2\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{777}}{2*7}=\frac{56-2\sqrt{777}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{777}}{2*7}=\frac{56+2\sqrt{777}}{14}
$