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(9x-1)(16x+6)=180
We move all terms to the left:
(9x-1)(16x+6)-(180)=0
We multiply parentheses ..
(+144x^2+54x-16x-6)-180=0
We get rid of parentheses
144x^2+54x-16x-6-180=0
We add all the numbers together, and all the variables
144x^2+38x-186=0
a = 144; b = 38; c = -186;
Δ = b2-4ac
Δ = 382-4·144·(-186)
Δ = 108580
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{108580}=\sqrt{4*27145}=\sqrt{4}*\sqrt{27145}=2\sqrt{27145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{27145}}{2*144}=\frac{-38-2\sqrt{27145}}{288} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{27145}}{2*144}=\frac{-38+2\sqrt{27145}}{288} $
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