2x-5=3(1/2x+4)

Solution for 2x-5=3(1/2x+4) equation:

2x-5=3(1/2x+4)

We move all terms to the left:

2x-5-(3(1/2x+4))=0


Domain of the equation: 2x+4))!=0

x∈R


We multiply all the terms by the denominator


2x*2x-5*2x+4))-(3(1+4))=0

We add all the numbers together, and all the variables

2x*2x-5*2x+4))-(35)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-10x=0

a = 4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·4·0
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*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*4}=\frac{20}{8}
=2+1/2
$