5x-3=3/8x-3

Solution for 5x-3=3/8x-3 equation:

5x-3=3/8x-3

We move all terms to the left:

5x-3-(3/8x-3)=0


Domain of the equation: 8x-3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


5x*8x+3*8x-3*8x-3=0

Wy multiply elements

40x^2+24x-24x-3=0

We add all the numbers together, and all the variables

40x^2-3=0

a = 40; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·40·(-3)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*40}=\frac{0-4\sqrt{30}}{80}
=-\frac{4\sqrt{30}}{80}
=-\frac{\sqrt{30}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*40}=\frac{0+4\sqrt{30}}{80}
=\frac{4\sqrt{30}}{80}
=\frac{\sqrt{30}}{20}
$