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(9x-4)(x+14)=180
We move all terms to the left:
(9x-4)(x+14)-(180)=0
We multiply parentheses ..
(+9x^2+126x-4x-56)-180=0
We get rid of parentheses
9x^2+126x-4x-56-180=0
We add all the numbers together, and all the variables
9x^2+122x-236=0
a = 9; b = 122; c = -236;
Δ = b2-4ac
Δ = 1222-4·9·(-236)
Δ = 23380
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23380}=\sqrt{4*5845}=\sqrt{4}*\sqrt{5845}=2\sqrt{5845}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-2\sqrt{5845}}{2*9}=\frac{-122-2\sqrt{5845}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+2\sqrt{5845}}{2*9}=\frac{-122+2\sqrt{5845}}{18} $
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