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60=x(x+8)
We move all terms to the left:
60-(x(x+8))=0
We calculate terms in parentheses: -(x(x+8)), so:We get rid of parentheses
x(x+8)
We multiply parentheses
x^2+8x
Back to the equation:
-(x^2+8x)
-x^2-8x+60=0
We add all the numbers together, and all the variables
-1x^2-8x+60=0
a = -1; b = -8; c = +60;
Δ = b2-4ac
Δ = -82-4·(-1)·60
Δ = 304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{19}}{2*-1}=\frac{8-4\sqrt{19}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{19}}{2*-1}=\frac{8+4\sqrt{19}}{-2} $
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