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(3x+5)(5x+5)+90=180
We move all terms to the left:
(3x+5)(5x+5)+90-(180)=0
We add all the numbers together, and all the variables
(3x+5)(5x+5)-90=0
We multiply parentheses ..
(+15x^2+15x+25x+25)-90=0
We get rid of parentheses
15x^2+15x+25x+25-90=0
We add all the numbers together, and all the variables
15x^2+40x-65=0
a = 15; b = 40; c = -65;
Δ = b2-4ac
Δ = 402-4·15·(-65)
Δ = 5500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5500}=\sqrt{100*55}=\sqrt{100}*\sqrt{55}=10\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{55}}{2*15}=\frac{-40-10\sqrt{55}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{55}}{2*15}=\frac{-40+10\sqrt{55}}{30} $
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