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8+3x(4x+9)=56
We move all terms to the left:
8+3x(4x+9)-(56)=0
We add all the numbers together, and all the variables
3x(4x+9)-48=0
We multiply parentheses
12x^2+27x-48=0
a = 12; b = 27; c = -48;
Δ = b2-4ac
Δ = 272-4·12·(-48)
Δ = 3033
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3033}=\sqrt{9*337}=\sqrt{9}*\sqrt{337}=3\sqrt{337}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{337}}{2*12}=\frac{-27-3\sqrt{337}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{337}}{2*12}=\frac{-27+3\sqrt{337}}{24} $
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