4(1/2x-3)=3(2/5x+6)

Solution for 4(1/2x-3)=3(2/5x+6) equation:

4(1/2x-3)=3(2/5x+6)

We move all terms to the left:

4(1/2x-3)-(3(2/5x+6))=0


Domain of the equation: 2x-3)!=0

x∈R



Domain of the equation: 5x+6))!=0

x∈R


We multiply parentheses

4x-(3(2/5x+6))-12=0

We multiply all the terms by the denominator


4x*5x-12*5x+6))-(3(2+6))=0

We add all the numbers together, and all the variables

4x*5x-12*5x+6))-(38)=0

We add all the numbers together, and all the variables

4x*5x-12*5x=0

Wy multiply elements

20x^2-60x=0

a = 20; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·20·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*20}=\frac{120}{40}
=3
$