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(4x+19)(6x+5)=180
We move all terms to the left:
(4x+19)(6x+5)-(180)=0
We multiply parentheses ..
(+24x^2+20x+114x+95)-180=0
We get rid of parentheses
24x^2+20x+114x+95-180=0
We add all the numbers together, and all the variables
24x^2+134x-85=0
a = 24; b = 134; c = -85;
Δ = b2-4ac
Δ = 1342-4·24·(-85)
Δ = 26116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26116}=\sqrt{4*6529}=\sqrt{4}*\sqrt{6529}=2\sqrt{6529}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-2\sqrt{6529}}{2*24}=\frac{-134-2\sqrt{6529}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+2\sqrt{6529}}{2*24}=\frac{-134+2\sqrt{6529}}{48} $
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