(5/2)(x)+(x-4)/2=11

Solution for (5/2)(x)+(x-4)/2=11 equation:

(5/2)(x)+(x-4)/2=11

We move all terms to the left:

(5/2)(x)+(x-4)/2-(11)=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

(+5/2)x+(x-4)/2-11=0

We multiply parentheses

5x^2+(x-4)/2-11=0

We multiply all the terms by the denominator


5x^2*2+(x-4)-11*2=0

We add all the numbers together, and all the variables

5x^2*2+(x-4)-22=0

Wy multiply elements

10x^2+(x-4)-22=0

We get rid of parentheses

10x^2+x-4-22=0

We add all the numbers together, and all the variables

10x^2+x-26=0

a = 10; b = 1; c = -26;
Δ = b2-4ac
Δ = 12-4·10·(-26)
Δ = 1041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1041}}{2*10}=\frac{-1-\sqrt{1041}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1041}}{2*10}=\frac{-1+\sqrt{1041}}{20}
$