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5*12=x(x+4)
We move all terms to the left:
5*12-(x(x+4))=0
We add all the numbers together, and all the variables
-(x(x+4))+60=0
We calculate terms in parentheses: -(x(x+4)), so:We get rid of parentheses
x(x+4)
We multiply parentheses
x^2+4x
Back to the equation:
-(x^2+4x)
-x^2-4x+60=0
We add all the numbers together, and all the variables
-1x^2-4x+60=0
a = -1; b = -4; c = +60;
Δ = b2-4ac
Δ = -42-4·(-1)·60
Δ = 256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*-1}=\frac{-12}{-2} =+6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*-1}=\frac{20}{-2} =-10 $
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