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(6x+10)(4x+30)=180
We move all terms to the left:
(6x+10)(4x+30)-(180)=0
We multiply parentheses ..
(+24x^2+180x+40x+300)-180=0
We get rid of parentheses
24x^2+180x+40x+300-180=0
We add all the numbers together, and all the variables
24x^2+220x+120=0
a = 24; b = 220; c = +120;
Δ = b2-4ac
Δ = 2202-4·24·120
Δ = 36880
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36880}=\sqrt{16*2305}=\sqrt{16}*\sqrt{2305}=4\sqrt{2305}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-4\sqrt{2305}}{2*24}=\frac{-220-4\sqrt{2305}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+4\sqrt{2305}}{2*24}=\frac{-220+4\sqrt{2305}}{48} $
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