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)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3x-1/28x-5-20=0

We multiply all the terms by the denominator


-3x*28x-5*28x-20*28x-1=0

Wy multiply elements

-84x^2-140x-560x-1=0

We add all the numbers together, and all the variables

-84x^2-700x-1=0

a = -84; b = -700; c = -1;
Δ = b2-4ac
Δ = -7002-4·(-84)·(-1)
Δ = 489664
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:

$\sqrt{\Delta}=\sqrt{489664}=\sqrt{64*7651}=\sqrt{64}*\sqrt{7651}=8\sqrt{7651}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-8\sqrt{7651}}{2*-84}=\frac{700-8\sqrt{7651}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+8\sqrt{7651}}{2*-84}=\frac{700+8\sqrt{7651}}{-168}
$