1/5x+8=7x-5

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

1/5x+8=7x-5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-7x+5+8=0

We multiply all the terms by the denominator


-7x*5x+5*5x+8*5x+1=0

Wy multiply elements

-35x^2+25x+40x+1=0

We add all the numbers together, and all the variables

-35x^2+65x+1=0

a = -35; b = 65; c = +1;
Δ = b2-4ac
Δ = 652-4·(-35)·1
Δ = 4365
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:

$\sqrt{\Delta}=\sqrt{4365}=\sqrt{9*485}=\sqrt{9}*\sqrt{485}=3\sqrt{485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-3\sqrt{485}}{2*-35}=\frac{-65-3\sqrt{485}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+3\sqrt{485}}{2*-35}=\frac{-65+3\sqrt{485}}{-70}
$