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

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

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

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

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