5(x-3)3x=8x-15-6x

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Solution for 5(x-3)3x=8x-15-6x equation:



5(x-3)3x=8x-15-6x
We move all terms to the left:
5(x-3)3x-(8x-15-6x)=0
We add all the numbers together, and all the variables
5(x-3)3x-(2x-15)=0
We multiply parentheses
15x^2-45x-(2x-15)=0
We get rid of parentheses
15x^2-45x-2x+15=0
We add all the numbers together, and all the variables
15x^2-47x+15=0
a = 15; b = -47; c = +15;
Δ = b2-4ac
Δ = -472-4·15·15
Δ = 1309
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{1309}}{2*15}=\frac{47-\sqrt{1309}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{1309}}{2*15}=\frac{47+\sqrt{1309}}{30} $

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