1.5(6x-3)7x=3(7-x)

Solution for 1.5(6x-3)7x=3(7-x) equation:

1.5(6x-3)7x=3(7-x)

We move all terms to the left:

1.5(6x-3)7x-(3(7-x))=0

We add all the numbers together, and all the variables

1.5(6x-3)7x-(3(-1x+7))=0

We multiply parentheses

60x^2-30x-(3(-1x+7))=0


We calculate terms in parentheses: -(3(-1x+7)), so:

3(-1x+7)

We multiply parentheses

-3x+21

Back to the equation:

-(-3x+21)


We get rid of parentheses

60x^2-30x+3x-21=0

We add all the numbers together, and all the variables

60x^2-27x-21=0

a = 60; b = -27; c = -21;
Δ = b2-4ac
Δ = -272-4·60·(-21)
Δ = 5769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5769}=\sqrt{9*641}=\sqrt{9}*\sqrt{641}=3\sqrt{641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{641}}{2*60}=\frac{27-3\sqrt{641}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{641}}{2*60}=\frac{27+3\sqrt{641}}{120}
$