(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


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

x+(+5/2)x-13=0

We multiply parentheses

5x^2+x-13=0

a = 5; b = 1; c = -13;
Δ = b2-4ac
Δ = 12-4·5·(-13)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{29}}{2*5}=\frac{-1-3\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{29}}{2*5}=\frac{-1+3\sqrt{29}}{10}
$