3x-5+7x2=3x2+7+11x

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Solution for 3x-5+7x2=3x2+7+11x equation:



3x-5+7x^2=3x^2+7+11x
We move all terms to the left:
3x-5+7x^2-(3x^2+7+11x)=0
We get rid of parentheses
7x^2-3x^2+3x-11x-7-5=0
We add all the numbers together, and all the variables
4x^2-8x-12=0
a = 4; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·4·(-12)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*4}=\frac{-8}{8} =-1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*4}=\frac{24}{8} =3 $

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