6-3(2x-3)=5(6-x)4x

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

6-3(2x-3)=5(6-x)4x

We move all terms to the left:

6-3(2x-3)-(5(6-x)4x)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-6x-(5(-1x+6)4x)+9+6=0


We calculate terms in parentheses: -(5(-1x+6)4x), so:

5(-1x+6)4x

We multiply parentheses

-20x^2+120x

Back to the equation:

-(-20x^2+120x)


We add all the numbers together, and all the variables

-(-20x^2+120x)-6x+15=0

We get rid of parentheses

20x^2-120x-6x+15=0

We add all the numbers together, and all the variables

20x^2-126x+15=0

a = 20; b = -126; c = +15;
Δ = b2-4ac
Δ = -1262-4·20·15
Δ = 14676
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:

$\sqrt{\Delta}=\sqrt{14676}=\sqrt{4*3669}=\sqrt{4}*\sqrt{3669}=2\sqrt{3669}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3669}}{2*20}=\frac{126-2\sqrt{3669}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3669}}{2*20}=\frac{126+2\sqrt{3669}}{40}
$