-15x+21=x(5x-7)

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Solution for -15x+21=x(5x-7) equation:



-15x+21=x(5x-7)
We move all terms to the left:
-15x+21-(x(5x-7))=0
We calculate terms in parentheses: -(x(5x-7)), so:
x(5x-7)
We multiply parentheses
5x^2-7x
Back to the equation:
-(5x^2-7x)
We get rid of parentheses
-5x^2-15x+7x+21=0
We add all the numbers together, and all the variables
-5x^2-8x+21=0
a = -5; b = -8; c = +21;
Δ = b2-4ac
Δ = -82-4·(-5)·21
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-22}{2*-5}=\frac{-14}{-10} =1+2/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*-5}=\frac{30}{-10} =-3 $

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