5x2=8x+21

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Solution for 5x2=8x+21 equation:



5x^2=8x+21
We move all terms to the left:
5x^2-(8x+21)=0
We get rid of parentheses
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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