-1/7x-4(1/7x-5)=-x+8

Solution for -1/7x-4(1/7x-5)=-x+8 equation:

-1/7x-4(1/7x-5)=-x+8

We move all terms to the left:

-1/7x-4(1/7x-5)-(-x+8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

-1/7x-4(1/7x-5)-(-1x+8)=0

We multiply parentheses

-1/7x-4x-(-1x+8)+20=0

We get rid of parentheses

-1/7x-4x+1x-8+20=0

We multiply all the terms by the denominator


-4x*7x+1x*7x-8*7x+20*7x-1=0

Wy multiply elements

-28x^2+7x^2-56x+140x-1=0

We add all the numbers together, and all the variables

-21x^2+84x-1=0

a = -21; b = 84; c = -1;
Δ = b2-4ac
Δ = 842-4·(-21)·(-1)
Δ = 6972
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:

$\sqrt{\Delta}=\sqrt{6972}=\sqrt{4*1743}=\sqrt{4}*\sqrt{1743}=2\sqrt{1743}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{1743}}{2*-21}=\frac{-84-2\sqrt{1743}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{1743}}{2*-21}=\frac{-84+2\sqrt{1743}}{-42}
$