8x(5x+2)=27

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Solution for 8x(5x+2)=27 equation:



8x(5x+2)=27
We move all terms to the left:
8x(5x+2)-(27)=0
We multiply parentheses
40x^2+16x-27=0
a = 40; b = 16; c = -27;
Δ = b2-4ac
Δ = 162-4·40·(-27)
Δ = 4576
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:
$\sqrt{\Delta}=\sqrt{4576}=\sqrt{16*286}=\sqrt{16}*\sqrt{286}=4\sqrt{286}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{286}}{2*40}=\frac{-16-4\sqrt{286}}{80} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{286}}{2*40}=\frac{-16+4\sqrt{286}}{80} $

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