2x2=6-5x

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Solution for 2x2=6-5x equation:



2x^2=6-5x
We move all terms to the left:
2x^2-(6-5x)=0
We add all the numbers together, and all the variables
2x^2-(-5x+6)=0
We get rid of parentheses
2x^2+5x-6=0
a = 2; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·2·(-6)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{73}}{2*2}=\frac{-5-\sqrt{73}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*2}=\frac{-5+\sqrt{73}}{4} $

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