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23+2x(3x+13)=180
We move all terms to the left:
23+2x(3x+13)-(180)=0
We add all the numbers together, and all the variables
2x(3x+13)-157=0
We multiply parentheses
6x^2+26x-157=0
a = 6; b = 26; c = -157;
Δ = b2-4ac
Δ = 262-4·6·(-157)
Δ = 4444
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4444}=\sqrt{4*1111}=\sqrt{4}*\sqrt{1111}=2\sqrt{1111}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1111}}{2*6}=\frac{-26-2\sqrt{1111}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1111}}{2*6}=\frac{-26+2\sqrt{1111}}{12} $
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