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(13x+1)(9x+3)=180
We move all terms to the left:
(13x+1)(9x+3)-(180)=0
We multiply parentheses ..
(+117x^2+39x+9x+3)-180=0
We get rid of parentheses
117x^2+39x+9x+3-180=0
We add all the numbers together, and all the variables
117x^2+48x-177=0
a = 117; b = 48; c = -177;
Δ = b2-4ac
Δ = 482-4·117·(-177)
Δ = 85140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{85140}=\sqrt{36*2365}=\sqrt{36}*\sqrt{2365}=6\sqrt{2365}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{2365}}{2*117}=\frac{-48-6\sqrt{2365}}{234} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{2365}}{2*117}=\frac{-48+6\sqrt{2365}}{234} $
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