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x+4x(3x+54)=180
We move all terms to the left:
x+4x(3x+54)-(180)=0
We multiply parentheses
12x^2+x+216x-180=0
We add all the numbers together, and all the variables
12x^2+217x-180=0
a = 12; b = 217; c = -180;
Δ = b2-4ac
Δ = 2172-4·12·(-180)
Δ = 55729
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(217)-\sqrt{55729}}{2*12}=\frac{-217-\sqrt{55729}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(217)+\sqrt{55729}}{2*12}=\frac{-217+\sqrt{55729}}{24} $
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