x=7/8(x)+4

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

x=7/8(x)+4

We move all terms to the left:

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


Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

x-7/8x-4=0

We multiply all the terms by the denominator


x*8x-4*8x-7=0

Wy multiply elements

8x^2-32x-7=0

a = 8; b = -32; c = -7;
Δ = b2-4ac
Δ = -322-4·8·(-7)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{78}}{2*8}=\frac{32-4\sqrt{78}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{78}}{2*8}=\frac{32+4\sqrt{78}}{16}
$