3(5-2x)=-2(6-3x)10x

Solution for 3(5-2x)=-2(6-3x)10x equation:

3(5-2x)=-2(6-3x)10x

We move all terms to the left:

3(5-2x)-(-2(6-3x)10x)=0

We add all the numbers together, and all the variables

3(-2x+5)-(-2(-3x+6)10x)=0

We multiply parentheses

-6x-(-2(-3x+6)10x)+15=0


We calculate terms in parentheses: -(-2(-3x+6)10x), so:

-2(-3x+6)10x

We multiply parentheses

60x^2-120x

Back to the equation:

-(60x^2-120x)


We get rid of parentheses

-60x^2-6x+120x+15=0

We add all the numbers together, and all the variables

-60x^2+114x+15=0

a = -60; b = 114; c = +15;
Δ = b2-4ac
Δ = 1142-4·(-60)·15
Δ = 16596
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:

$\sqrt{\Delta}=\sqrt{16596}=\sqrt{36*461}=\sqrt{36}*\sqrt{461}=6\sqrt{461}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-6\sqrt{461}}{2*-60}=\frac{-114-6\sqrt{461}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+6\sqrt{461}}{2*-60}=\frac{-114+6\sqrt{461}}{-120}
$