19x2-18x-18=10x2-9

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Solution for 19x2-18x-18=10x2-9 equation:



19x^2-18x-18=10x^2-9
We move all terms to the left:
19x^2-18x-18-(10x^2-9)=0
We get rid of parentheses
19x^2-10x^2-18x+9-18=0
We add all the numbers together, and all the variables
9x^2-18x-9=0
a = 9; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·9·(-9)
Δ = 648
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:
$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{2}}{2*9}=\frac{18-18\sqrt{2}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{2}}{2*9}=\frac{18+18\sqrt{2}}{18} $

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