7x-3x+5-8=1/28x+20-7x+5

Solution for 7x-3x+5-8=1/28x+20-7x+5 equation:

7x-3x+5-8=1/28x+20-7x+5

We move all terms to the left:

7x-3x+5-8-(1/28x+20-7x+5)=0


Domain of the equation: 28x+20-7x+5)!=0

We move all terms containing x to the left, all other terms to the right

28x-7x+5)!=-20

x∈R


We add all the numbers together, and all the variables

7x-3x-(-7x+1/28x+25)+5-8=0

We add all the numbers together, and all the variables

4x-(-7x+1/28x+25)-3=0

We get rid of parentheses

4x+7x-1/28x-25-3=0

We multiply all the terms by the denominator


4x*28x+7x*28x-25*28x-3*28x-1=0

Wy multiply elements

112x^2+196x^2-700x-84x-1=0

We add all the numbers together, and all the variables

308x^2-784x-1=0

a = 308; b = -784; c = -1;
Δ = b2-4ac
Δ = -7842-4·308·(-1)
Δ = 615888
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:

$\sqrt{\Delta}=\sqrt{615888}=\sqrt{144*4277}=\sqrt{144}*\sqrt{4277}=12\sqrt{4277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-784)-12\sqrt{4277}}{2*308}=\frac{784-12\sqrt{4277}}{616}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-784)+12\sqrt{4277}}{2*308}=\frac{784+12\sqrt{4277}}{616}
$