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x(x-15)=18
We move all terms to the left:
x(x-15)-(18)=0
We multiply parentheses
x^2-15x-18=0
a = 1; b = -15; c = -18;
Δ = b2-4ac
Δ = -152-4·1·(-18)
Δ = 297
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{33}}{2*1}=\frac{15-3\sqrt{33}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{33}}{2*1}=\frac{15+3\sqrt{33}}{2} $
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