6x^2+5=13x

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Solution for 6x^2+5=13x equation:



6x^2+5=13x
We move all terms to the left:
6x^2+5-(13x)=0
a = 6; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·6·5
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*6}=\frac{6}{12} =1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*6}=\frac{20}{12} =1+2/3 $

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