21/4x+.5x=44

Solution for 21/4x+.5x=44 equation:

21/4x+.5x=44

We move all terms to the left:

21/4x+.5x-(44)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

.5x+21/4x-44=0

We multiply all the terms by the denominator


(.5x)*4x-44*4x+21=0

We add all the numbers together, and all the variables

(+.5x)*4x-44*4x+21=0

We multiply parentheses

4x^2-44*4x+21=0

Wy multiply elements

4x^2-176x+21=0

a = 4; b = -176; c = +21;
Δ = b2-4ac
Δ = -1762-4·4·21
Δ = 30640
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:

$\sqrt{\Delta}=\sqrt{30640}=\sqrt{16*1915}=\sqrt{16}*\sqrt{1915}=4\sqrt{1915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1915}}{2*4}=\frac{176-4\sqrt{1915}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1915}}{2*4}=\frac{176+4\sqrt{1915}}{8}
$