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X2-10X-18=25
We move all terms to the left:
X2-10X-18-(25)=0
We add all the numbers together, and all the variables
X^2-10X-43=0
a = 1; b = -10; c = -43;
Δ = b2-4ac
Δ = -102-4·1·(-43)
Δ = 272
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{17}}{2*1}=\frac{10-4\sqrt{17}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{17}}{2*1}=\frac{10+4\sqrt{17}}{2} $
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