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x^2-6x+5x-28=180
We move all terms to the left:
x^2-6x+5x-28-(180)=0
We add all the numbers together, and all the variables
x^2-1x-208=0
a = 1; b = -1; c = -208;
Δ = b2-4ac
Δ = -12-4·1·(-208)
Δ = 833
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7\sqrt{17}}{2*1}=\frac{1-7\sqrt{17}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7\sqrt{17}}{2*1}=\frac{1+7\sqrt{17}}{2} $
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