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9x+18=5x^2-180
We move all terms to the left:
9x+18-(5x^2-180)=0
We get rid of parentheses
-5x^2+9x+180+18=0
We add all the numbers together, and all the variables
-5x^2+9x+198=0
a = -5; b = 9; c = +198;
Δ = b2-4ac
Δ = 92-4·(-5)·198
Δ = 4041
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4041}=\sqrt{9*449}=\sqrt{9}*\sqrt{449}=3\sqrt{449}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{449}}{2*-5}=\frac{-9-3\sqrt{449}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{449}}{2*-5}=\frac{-9+3\sqrt{449}}{-10} $
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