(x+5)*3=x(5x-17)

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Solution for (x+5)*3=x(5x-17) equation:



(x+5)*3=x(5x-17)
We move all terms to the left:
(x+5)*3-(x(5x-17))=0
We multiply parentheses
3x-(x(5x-17))+15=0
We calculate terms in parentheses: -(x(5x-17)), so:
x(5x-17)
We multiply parentheses
5x^2-17x
Back to the equation:
-(5x^2-17x)
We get rid of parentheses
-5x^2+3x+17x+15=0
We add all the numbers together, and all the variables
-5x^2+20x+15=0
a = -5; b = 20; c = +15;
Δ = b2-4ac
Δ = 202-4·(-5)·15
Δ = 700
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:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{7}}{2*-5}=\frac{-20-10\sqrt{7}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{7}}{2*-5}=\frac{-20+10\sqrt{7}}{-10} $

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