x=3/8x+110

Solution for x=3/8x+110 equation:

x=3/8x+110

We move all terms to the left:

x-(3/8x+110)=0


Domain of the equation: 8x+110)!=0

x∈R


We get rid of parentheses

x-3/8x-110=0

We multiply all the terms by the denominator


x*8x-110*8x-3=0

Wy multiply elements

8x^2-880x-3=0

a = 8; b = -880; c = -3;
Δ = b2-4ac
Δ = -8802-4·8·(-3)
Δ = 774496
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:

$\sqrt{\Delta}=\sqrt{774496}=\sqrt{16*48406}=\sqrt{16}*\sqrt{48406}=4\sqrt{48406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-880)-4\sqrt{48406}}{2*8}=\frac{880-4\sqrt{48406}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-880)+4\sqrt{48406}}{2*8}=\frac{880+4\sqrt{48406}}{16}
$