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(6x+9)(4x-19)=180
We move all terms to the left:
(6x+9)(4x-19)-(180)=0
We multiply parentheses ..
(+24x^2-114x+36x-171)-180=0
We get rid of parentheses
24x^2-114x+36x-171-180=0
We add all the numbers together, and all the variables
24x^2-78x-351=0
a = 24; b = -78; c = -351;
Δ = b2-4ac
Δ = -782-4·24·(-351)
Δ = 39780
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39780}=\sqrt{36*1105}=\sqrt{36}*\sqrt{1105}=6\sqrt{1105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-6\sqrt{1105}}{2*24}=\frac{78-6\sqrt{1105}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+6\sqrt{1105}}{2*24}=\frac{78+6\sqrt{1105}}{48} $
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