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-115+30x-x^2=0
We add all the numbers together, and all the variables
-1x^2+30x-115=0
a = -1; b = 30; c = -115;
Δ = b2-4ac
Δ = 302-4·(-1)·(-115)
Δ = 440
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{110}}{2*-1}=\frac{-30-2\sqrt{110}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{110}}{2*-1}=\frac{-30+2\sqrt{110}}{-2} $
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