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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2+1*8x+3*8x-5=0

Wy multiply elements

8x^2+8x+24x-5=0

We add all the numbers together, and all the variables

8x^2+32x-5=0

a = 8; b = 32; c = -5;
Δ = b2-4ac
Δ = 322-4·8·(-5)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{74}}{2*8}=\frac{-32-4\sqrt{74}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{74}}{2*8}=\frac{-32+4\sqrt{74}}{16}
$