(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 calculate terms in parentheses: +((x-4)2), so:

(x-4)2

We multiply parentheses

2x-8

Back to the equation:

+(2x-8)


We get rid of parentheses

5x^2+2x-8-11=0

We add all the numbers together, and all the variables

5x^2+2x-19=0

a = 5; b = 2; c = -19;
Δ = b2-4ac
Δ = 22-4·5·(-19)
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{-(2)-8\sqrt{6}}{2*5}=\frac{-2-8\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{6}}{2*5}=\frac{-2+8\sqrt{6}}{10}
$