(3/4)x=27/28

Solution for (3/4)x=27/28 equation:

(3/4)x=27/28

We move all terms to the left:

(3/4)x-(27/28)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)x-(+27/28)=0

We multiply parentheses

3x^2-(+27/28)=0

We get rid of parentheses

3x^2-27/28=0

We multiply all the terms by the denominator


3x^2*28-27=0

Wy multiply elements

84x^2-27=0

a = 84; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·84·(-27)
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{7}}{2*84}=\frac{0-36\sqrt{7}}{168}
=-\frac{36\sqrt{7}}{168}
=-\frac{3\sqrt{7}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{7}}{2*84}=\frac{0+36\sqrt{7}}{168}
=\frac{36\sqrt{7}}{168}
=\frac{3\sqrt{7}}{14}
$