x=10+5/7x+8

Solution for x=10+5/7x+8 equation:

x=10+5/7x+8

We move all terms to the left:

x-(10+5/7x+8)=0


Domain of the equation: 7x+8)!=0

x∈R


We add all the numbers together, and all the variables

x-(5/7x+18)=0

We get rid of parentheses

x-5/7x-18=0

We multiply all the terms by the denominator


x*7x-18*7x-5=0

Wy multiply elements

7x^2-126x-5=0

a = 7; b = -126; c = -5;
Δ = b2-4ac
Δ = -1262-4·7·(-5)
Δ = 16016
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:

$\sqrt{\Delta}=\sqrt{16016}=\sqrt{16*1001}=\sqrt{16}*\sqrt{1001}=4\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-4\sqrt{1001}}{2*7}=\frac{126-4\sqrt{1001}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+4\sqrt{1001}}{2*7}=\frac{126+4\sqrt{1001}}{14}
$