5x(3x+38)=x

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Solution for 5x(3x+38)=x equation:



5x(3x+38)=x
We move all terms to the left:
5x(3x+38)-(x)=0
We add all the numbers together, and all the variables
-1x+5x(3x+38)=0
We multiply parentheses
15x^2-1x+190x=0
We add all the numbers together, and all the variables
15x^2+189x=0
a = 15; b = 189; c = 0;
Δ = b2-4ac
Δ = 1892-4·15·0
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(189)-189}{2*15}=\frac{-378}{30} =-12+3/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(189)+189}{2*15}=\frac{0}{30} =0 $

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