x^2+2x/2=2.5

Solution for x^2+2x/2=2.5 equation:

x^2+2x/2=2.5

We move all terms to the left:

x^2+2x/2-(2.5)=0

We add all the numbers together, and all the variables

x^2+2x/2-2.5=0

We multiply all the terms by the denominator


x^2*2+2x-(2.5)*2=0

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2+2x-5=0

a = 2; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·2·(-5)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{11}}{2*2}=\frac{-2-2\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{11}}{2*2}=\frac{-2+2\sqrt{11}}{4}
$