10(x/2)=3/4x

Solution for 10(x/2)=3/4x equation:

10(x/2)=3/4x

We move all terms to the left:

10(x/2)-(3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10(+x/2)-(+3/4x)=0

We multiply parentheses

10x-(+3/4x)=0

We get rid of parentheses

10x-3/4x=0

We multiply all the terms by the denominator


10x*4x-3=0

Wy multiply elements

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}
$