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((10x)(9x+3))/2=360
We move all terms to the left:
((10x)(9x+3))/2-(360)=0
We multiply all the terms by the denominator
(10x(9x+3))-360*2=0
We calculate terms in parentheses: +(10x(9x+3)), so:We add all the numbers together, and all the variables
10x(9x+3)
We multiply parentheses
90x^2+30x
Back to the equation:
+(90x^2+30x)
(90x^2+30x)-720=0
We get rid of parentheses
90x^2+30x-720=0
a = 90; b = 30; c = -720;
Δ = b2-4ac
Δ = 302-4·90·(-720)
Δ = 260100
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{260100}=510$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-510}{2*90}=\frac{-540}{180} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+510}{2*90}=\frac{480}{180} =2+2/3 $
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