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3x(2x+13)+57=180
We move all terms to the left:
3x(2x+13)+57-(180)=0
We add all the numbers together, and all the variables
3x(2x+13)-123=0
We multiply parentheses
6x^2+39x-123=0
a = 6; b = 39; c = -123;
Δ = b2-4ac
Δ = 392-4·6·(-123)
Δ = 4473
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4473}=\sqrt{9*497}=\sqrt{9}*\sqrt{497}=3\sqrt{497}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{497}}{2*6}=\frac{-39-3\sqrt{497}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{497}}{2*6}=\frac{-39+3\sqrt{497}}{12} $
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