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3x(4x+68)+7=-180
We move all terms to the left:
3x(4x+68)+7-(-180)=0
We add all the numbers together, and all the variables
3x(4x+68)+187=0
We multiply parentheses
12x^2+204x+187=0
a = 12; b = 204; c = +187;
Δ = b2-4ac
Δ = 2042-4·12·187
Δ = 32640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32640}=\sqrt{64*510}=\sqrt{64}*\sqrt{510}=8\sqrt{510}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(204)-8\sqrt{510}}{2*12}=\frac{-204-8\sqrt{510}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(204)+8\sqrt{510}}{2*12}=\frac{-204+8\sqrt{510}}{24} $
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