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(x+10)(x+30)=180
We move all terms to the left:
(x+10)(x+30)-(180)=0
We multiply parentheses ..
(+x^2+30x+10x+300)-180=0
We get rid of parentheses
x^2+30x+10x+300-180=0
We add all the numbers together, and all the variables
x^2+40x+120=0
a = 1; b = 40; c = +120;
Δ = b2-4ac
Δ = 402-4·1·120
Δ = 1120
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{70}}{2*1}=\frac{-40-4\sqrt{70}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{70}}{2*1}=\frac{-40+4\sqrt{70}}{2} $
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