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12x+17=x2
We move all terms to the left:
12x+17-(x2)=0
We add all the numbers together, and all the variables
-1x^2+12x+17=0
a = -1; b = 12; c = +17;
Δ = b2-4ac
Δ = 122-4·(-1)·17
Δ = 212
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{53}}{2*-1}=\frac{-12-2\sqrt{53}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{53}}{2*-1}=\frac{-12+2\sqrt{53}}{-2} $
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