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84+(4x)(5x+3)=180
We move all terms to the left:
84+(4x)(5x+3)-(180)=0
We add all the numbers together, and all the variables
4x(5x+3)-96=0
We multiply parentheses
20x^2+12x-96=0
a = 20; b = 12; c = -96;
Δ = b2-4ac
Δ = 122-4·20·(-96)
Δ = 7824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7824}=\sqrt{16*489}=\sqrt{16}*\sqrt{489}=4\sqrt{489}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{489}}{2*20}=\frac{-12-4\sqrt{489}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{489}}{2*20}=\frac{-12+4\sqrt{489}}{40} $
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