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x2-7+6x+20=180
We move all terms to the left:
x2-7+6x+20-(180)=0
We add all the numbers together, and all the variables
x^2+6x-167=0
a = 1; b = 6; c = -167;
Δ = b2-4ac
Δ = 62-4·1·(-167)
Δ = 704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8\sqrt{11}}{2*1}=\frac{-6-8\sqrt{11}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8\sqrt{11}}{2*1}=\frac{-6+8\sqrt{11}}{2} $
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