5x+3=5(x+1)x

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Solution for 5x+3=5(x+1)x equation:



5x+3=5(x+1)x
We move all terms to the left:
5x+3-(5(x+1)x)=0
We calculate terms in parentheses: -(5(x+1)x), so:
5(x+1)x
We multiply parentheses
5x^2+5x
Back to the equation:
-(5x^2+5x)
We get rid of parentheses
-5x^2+5x-5x+3=0
We add all the numbers together, and all the variables
-5x^2+3=0
a = -5; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-5)·3
Δ = 60
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:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-5}=\frac{0-2\sqrt{15}}{-10} =-\frac{2\sqrt{15}}{-10} =-\frac{\sqrt{15}}{-5} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-5}=\frac{0+2\sqrt{15}}{-10} =\frac{2\sqrt{15}}{-10} =\frac{\sqrt{15}}{-5} $

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