2x^2+7x^2+6x+8+10=180

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Solution for 2x^2+7x^2+6x+8+10=180 equation:



2x^2+7x^2+6x+8+10=180
We move all terms to the left:
2x^2+7x^2+6x+8+10-(180)=0
We add all the numbers together, and all the variables
9x^2+6x-162=0
a = 9; b = 6; c = -162;
Δ = b2-4ac
Δ = 62-4·9·(-162)
Δ = 5868
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:
$\sqrt{\Delta}=\sqrt{5868}=\sqrt{36*163}=\sqrt{36}*\sqrt{163}=6\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{163}}{2*9}=\frac{-6-6\sqrt{163}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{163}}{2*9}=\frac{-6+6\sqrt{163}}{18} $

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