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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+2))!=0

x∈R


We multiply all the terms by the denominator


4x*2x-5*2x+2))-(2(1+2))=0

We add all the numbers together, and all the variables

4x*2x-5*2x+2))-(23)=0

We add all the numbers together, and all the variables

4x*2x-5*2x=0

Wy multiply elements

8x^2-10x=0

a = 8; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·8·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*8}=\frac{20}{16}
=1+1/4
$