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(6x+12)(7x+4)=180
We move all terms to the left:
(6x+12)(7x+4)-(180)=0
We multiply parentheses ..
(+42x^2+24x+84x+48)-180=0
We get rid of parentheses
42x^2+24x+84x+48-180=0
We add all the numbers together, and all the variables
42x^2+108x-132=0
a = 42; b = 108; c = -132;
Δ = b2-4ac
Δ = 1082-4·42·(-132)
Δ = 33840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{33840}=\sqrt{144*235}=\sqrt{144}*\sqrt{235}=12\sqrt{235}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-12\sqrt{235}}{2*42}=\frac{-108-12\sqrt{235}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+12\sqrt{235}}{2*42}=\frac{-108+12\sqrt{235}}{84} $
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