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(3x+40)(4x+20)=180
We move all terms to the left:
(3x+40)(4x+20)-(180)=0
We multiply parentheses ..
(+12x^2+60x+160x+800)-180=0
We get rid of parentheses
12x^2+60x+160x+800-180=0
We add all the numbers together, and all the variables
12x^2+220x+620=0
a = 12; b = 220; c = +620;
Δ = b2-4ac
Δ = 2202-4·12·620
Δ = 18640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18640}=\sqrt{16*1165}=\sqrt{16}*\sqrt{1165}=4\sqrt{1165}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-4\sqrt{1165}}{2*12}=\frac{-220-4\sqrt{1165}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+4\sqrt{1165}}{2*12}=\frac{-220+4\sqrt{1165}}{24} $
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