x-3/8x=-10

Solution for x-3/8x=-10 equation:

x-3/8x=-10

We move all terms to the left:

x-3/8x-(-10)=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}
$