4(3x-5)=-6(-5/3x+8)-6

Solution for 4(3x-5)=-6(-5/3x+8)-6 equation:

4(3x-5)=-6(-5/3x+8)-6

We move all terms to the left:

4(3x-5)-(-6(-5/3x+8)-6)=0


Domain of the equation: 3x+8)-6)!=0

x∈R


We multiply parentheses

12x-(-6(-5/3x+8)-6)-20=0

We multiply all the terms by the denominator


12x*3x-20*3x-5+8)-6)-(-6(+8)-6)=0

We add all the numbers together, and all the variables

12x*3x-20*3x-5+8)-6)-(-68-6)=0

We add all the numbers together, and all the variables

12x*3x-20*3x=0

Wy multiply elements

36x^2-60x=0

a = 36; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·36·0
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*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*36}=\frac{120}{72}
=1+2/3
$