.5x+2=3/8x-1

Solution for .5x+2=3/8x-1 equation:

.5x+2=3/8x-1

We move all terms to the left:

.5x+2-(3/8x-1)=0


Domain of the equation: 8x-1)!=0

x∈R


We get rid of parentheses

.5x-3/8x+1+2=0

We multiply all the terms by the denominator


(.5x)*8x+1*8x+2*8x-3=0

We add all the numbers together, and all the variables

(+.5x)*8x+1*8x+2*8x-3=0

We multiply parentheses

8x^2+1*8x+2*8x-3=0

Wy multiply elements

8x^2+8x+16x-3=0

We add all the numbers together, and all the variables

8x^2+24x-3=0

a = 8; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·8·(-3)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{42}}{2*8}=\frac{-24-4\sqrt{42}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{42}}{2*8}=\frac{-24+4\sqrt{42}}{16}
$