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(7x+1)(15x+3)=180
We move all terms to the left:
(7x+1)(15x+3)-(180)=0
We multiply parentheses ..
(+105x^2+21x+15x+3)-180=0
We get rid of parentheses
105x^2+21x+15x+3-180=0
We add all the numbers together, and all the variables
105x^2+36x-177=0
a = 105; b = 36; c = -177;
Δ = b2-4ac
Δ = 362-4·105·(-177)
Δ = 75636
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{75636}=\sqrt{36*2101}=\sqrt{36}*\sqrt{2101}=6\sqrt{2101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{2101}}{2*105}=\frac{-36-6\sqrt{2101}}{210} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{2101}}{2*105}=\frac{-36+6\sqrt{2101}}{210} $
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