x=7/8x+5

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

x=7/8x+5

We move all terms to the left:

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


Domain of the equation: 8x+5)!=0

x∈R


We get rid of parentheses

x-7/8x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-40x-7=0

a = 8; b = -40; c = -7;
Δ = b2-4ac
Δ = -402-4·8·(-7)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{114}}{2*8}=\frac{40-4\sqrt{114}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{114}}{2*8}=\frac{40+4\sqrt{114}}{16}
$