(4/5)*x=3/4

Solution for (4/5)*x=3/4 equation:

(4/5)*x=3/4

We move all terms to the left:

(4/5)*x-(3/4)=0


Domain of the equation: 5)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/5)*x-(+3/4)=0

We multiply parentheses

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

We get rid of parentheses

4x^2-3/4=0

We multiply all the terms by the denominator


4x^2*4-3=0

Wy multiply elements

16x^2-3=0

a = 16; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·16·(-3)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*16}=\frac{0-8\sqrt{3}}{32}
=-\frac{8\sqrt{3}}{32}
=-\frac{\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*16}=\frac{0+8\sqrt{3}}{32}
=\frac{8\sqrt{3}}{32}
=\frac{\sqrt{3}}{4}
$