2x(5X-9)=21

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Solution for 2x(5X-9)=21 equation:



2x(5x-9)=21
We move all terms to the left:
2x(5x-9)-(21)=0
We multiply parentheses
10x^2-18x-21=0
a = 10; b = -18; c = -21;
Δ = b2-4ac
Δ = -182-4·10·(-21)
Δ = 1164
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:
$\sqrt{\Delta}=\sqrt{1164}=\sqrt{4*291}=\sqrt{4}*\sqrt{291}=2\sqrt{291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{291}}{2*10}=\frac{18-2\sqrt{291}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{291}}{2*10}=\frac{18+2\sqrt{291}}{20} $

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