(2x+8)+(3x-14)(3x-14)=180

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Solution for (2x+8)+(3x-14)(3x-14)=180 equation:



(2x+8)+(3x-14)(3x-14)=180
We move all terms to the left:
(2x+8)+(3x-14)(3x-14)-(180)=0
We get rid of parentheses
2x+(3x-14)(3x-14)+8-180=0
We multiply parentheses ..
(+9x^2-42x-42x+196)+2x+8-180=0
We add all the numbers together, and all the variables
(+9x^2-42x-42x+196)+2x-172=0
We get rid of parentheses
9x^2-42x-42x+2x+196-172=0
We add all the numbers together, and all the variables
9x^2-82x+24=0
a = 9; b = -82; c = +24;
Δ = b2-4ac
Δ = -822-4·9·24
Δ = 5860
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:
$\sqrt{\Delta}=\sqrt{5860}=\sqrt{4*1465}=\sqrt{4}*\sqrt{1465}=2\sqrt{1465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1465}}{2*9}=\frac{82-2\sqrt{1465}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1465}}{2*9}=\frac{82+2\sqrt{1465}}{18} $

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