19x=-3x(5x+2)

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Solution for 19x=-3x(5x+2) equation:



19x=-3x(5x+2)
We move all terms to the left:
19x-(-3x(5x+2))=0
We calculate terms in parentheses: -(-3x(5x+2)), so:
-3x(5x+2)
We multiply parentheses
-15x^2-6x
Back to the equation:
-(-15x^2-6x)
We get rid of parentheses
15x^2+6x+19x=0
We add all the numbers together, and all the variables
15x^2+25x=0
a = 15; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·15·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*15}=\frac{-50}{30} =-1+2/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*15}=\frac{0}{30} =0 $

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