(5/2)x+(1/4)x=9/4+4x

Solution for (5/2)x+(1/4)x=9/4+4x equation:

(5/2)x+(1/4)x=9/4+4x

We move all terms to the left:

(5/2)x+(1/4)x-(9/4+4x)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4+4x)!=0

We move all terms containing x to the left, all other terms to the right

4x)!=-4

x!=-4/1

x!=-4

x∈R


We add all the numbers together, and all the variables

(+5/2)x+(+1/4)x-(+4x+9/4)=0

We multiply parentheses

5x^2+x^2-(+4x+9/4)=0

We get rid of parentheses

5x^2+x^2-4x-9/4=0

We multiply all the terms by the denominator


5x^2*4+x^2*4-4x*4-9=0

Wy multiply elements

20x^2+4x^2-16x-9=0

We add all the numbers together, and all the variables

24x^2-16x-9=0

a = 24; b = -16; c = -9;
Δ = b2-4ac
Δ = -162-4·24·(-9)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{70}}{2*24}=\frac{16-4\sqrt{70}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{70}}{2*24}=\frac{16+4\sqrt{70}}{48}
$