-3/8x+9+x=19

Solution for -3/8x+9+x=19 equation:

-3/8x+9+x=19

We move all terms to the left:

-3/8x+9+x-(19)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

x-3/8x-10=0

We multiply all the terms by the denominator


x*8x-10*8x-3=0

Wy multiply elements

8x^2-80x-3=0

a = 8; b = -80; c = -3;
Δ = b2-4ac
Δ = -802-4·8·(-3)
Δ = 6496
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:

$\sqrt{\Delta}=\sqrt{6496}=\sqrt{16*406}=\sqrt{16}*\sqrt{406}=4\sqrt{406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{406}}{2*8}=\frac{80-4\sqrt{406}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{406}}{2*8}=\frac{80+4\sqrt{406}}{16}
$