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

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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} $

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