7x-9x2=5x-2

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Solution for 7x-9x2=5x-2 equation:



7x-9x^2=5x-2
We move all terms to the left:
7x-9x^2-(5x-2)=0
We get rid of parentheses
-9x^2+7x-5x+2=0
We add all the numbers together, and all the variables
-9x^2+2x+2=0
a = -9; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-9)·2
Δ = 76
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:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*-9}=\frac{-2-2\sqrt{19}}{-18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*-9}=\frac{-2+2\sqrt{19}}{-18} $

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