4(x-5)=6(2-1/2x)

Solution for 4(x-5)=6(2-1/2x) equation:

4(x-5)=6(2-1/2x)

We move all terms to the left:

4(x-5)-(6(2-1/2x))=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(x-5)-(6(-1/2x+2))=0

We multiply parentheses

4x-(6(-1/2x+2))-20=0

We multiply all the terms by the denominator


4x*2x-20*2x-1+2))-(6(+2))=0

We add all the numbers together, and all the variables

4x*2x-20*2x-1+2))-(62)=0

We add all the numbers together, and all the variables

4x*2x-20*2x=0

Wy multiply elements

8x^2-40x=0

a = 8; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·8·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*8}=\frac{80}{16}
=5
$