3x2+2x-7=2x=5

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Solution for 3x2+2x-7=2x=5 equation:



3x^2+2x-7=2x=5
We move all terms to the left:
3x^2+2x-7-(2x)=0
We add all the numbers together, and all the variables
3x^2-7=0
a = 3; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·3·(-7)
Δ = 84
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:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*3}=\frac{0-2\sqrt{21}}{6} =-\frac{2\sqrt{21}}{6} =-\frac{\sqrt{21}}{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*3}=\frac{0+2\sqrt{21}}{6} =\frac{2\sqrt{21}}{6} =\frac{\sqrt{21}}{3} $

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