0.5x-7/8x=3

Solution for 0.5x-7/8x=3 equation:

0.5x-7/8x=3

We move all terms to the left:

0.5x-7/8x-(3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


(0.5x)*8x-3*8x-7=0

We add all the numbers together, and all the variables

(+0.5x)*8x-3*8x-7=0

We multiply parentheses

0x^2-3*8x-7=0

Wy multiply elements

0x^2-24x-7=0

We add all the numbers together, and all the variables

x^2-24x-7=0

a = 1; b = -24; c = -7;
Δ = b2-4ac
Δ = -242-4·1·(-7)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{151}}{2*1}=\frac{24-2\sqrt{151}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{151}}{2*1}=\frac{24+2\sqrt{151}}{2}
$