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(3x+)(5x+30)+65=180
We move all terms to the left:
(3x+)(5x+30)+65-(180)=0
We add all the numbers together, and all the variables
(+3x)(5x+30)+65-180=0
We add all the numbers together, and all the variables
(+3x)(5x+30)-115=0
We multiply parentheses ..
(+15x^2+90x)-115=0
We get rid of parentheses
15x^2+90x-115=0
a = 15; b = 90; c = -115;
Δ = b2-4ac
Δ = 902-4·15·(-115)
Δ = 15000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15000}=\sqrt{2500*6}=\sqrt{2500}*\sqrt{6}=50\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-50\sqrt{6}}{2*15}=\frac{-90-50\sqrt{6}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+50\sqrt{6}}{2*15}=\frac{-90+50\sqrt{6}}{30} $
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