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(2a-9)(5a+14)=180
We move all terms to the left:
(2a-9)(5a+14)-(180)=0
We multiply parentheses ..
(+10a^2+28a-45a-126)-180=0
We get rid of parentheses
10a^2+28a-45a-126-180=0
We add all the numbers together, and all the variables
10a^2-17a-306=0
a = 10; b = -17; c = -306;
Δ = b2-4ac
Δ = -172-4·10·(-306)
Δ = 12529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{12529}}{2*10}=\frac{17-\sqrt{12529}}{20} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{12529}}{2*10}=\frac{17+\sqrt{12529}}{20} $
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