(1/2)x+3/4=27/4

Solution for (1/2)x+3/4=27/4 equation:

(1/2)x+3/4=27/4

We move all terms to the left:

(1/2)x+3/4-(27/4)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x+3/4-(+27/4)=0

We multiply parentheses

x^2+3/4-(+27/4)=0

We get rid of parentheses

x^2+3/4-27/4=0

We multiply all the terms by the denominator


x^2*4+3-27=0

We add all the numbers together, and all the variables

x^2*4-24=0

Wy multiply elements

4x^2-24=0

a = 4; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·4·(-24)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*4}=\frac{0-8\sqrt{6}}{8}
=-\frac{8\sqrt{6}}{8}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*4}=\frac{0+8\sqrt{6}}{8}
=\frac{8\sqrt{6}}{8}
=\sqrt{6}
$