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180=(30+x)x
We move all terms to the left:
180-((30+x)x)=0
We add all the numbers together, and all the variables
-((x+30)x)+180=0
We calculate terms in parentheses: -((x+30)x), so:We get rid of parentheses
(x+30)x
We multiply parentheses
x^2+30x
Back to the equation:
-(x^2+30x)
-x^2-30x+180=0
We add all the numbers together, and all the variables
-1x^2-30x+180=0
a = -1; b = -30; c = +180;
Δ = b2-4ac
Δ = -302-4·(-1)·180
Δ = 1620
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{5}}{2*-1}=\frac{30-18\sqrt{5}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{5}}{2*-1}=\frac{30+18\sqrt{5}}{-2} $
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