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(3x+5)(5x+15)=180
We move all terms to the left:
(3x+5)(5x+15)-(180)=0
We multiply parentheses ..
(+15x^2+45x+25x+75)-180=0
We get rid of parentheses
15x^2+45x+25x+75-180=0
We add all the numbers together, and all the variables
15x^2+70x-105=0
a = 15; b = 70; c = -105;
Δ = b2-4ac
Δ = 702-4·15·(-105)
Δ = 11200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-40\sqrt{7}}{2*15}=\frac{-70-40\sqrt{7}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+40\sqrt{7}}{2*15}=\frac{-70+40\sqrt{7}}{30} $
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