7x^2=18x^2+3x-6

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Solution for 7x^2=18x^2+3x-6 equation:



7x^2=18x^2+3x-6
We move all terms to the left:
7x^2-(18x^2+3x-6)=0
We get rid of parentheses
7x^2-18x^2-3x+6=0
We add all the numbers together, and all the variables
-11x^2-3x+6=0
a = -11; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-11)·6
Δ = 273
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{-(-3)-\sqrt{273}}{2*-11}=\frac{3-\sqrt{273}}{-22} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{273}}{2*-11}=\frac{3+\sqrt{273}}{-22} $

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