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(x-14)(9x-4)=180
We move all terms to the left:
(x-14)(9x-4)-(180)=0
We multiply parentheses ..
(+9x^2-4x-126x+56)-180=0
We get rid of parentheses
9x^2-4x-126x+56-180=0
We add all the numbers together, and all the variables
9x^2-130x-124=0
a = 9; b = -130; c = -124;
Δ = b2-4ac
Δ = -1302-4·9·(-124)
Δ = 21364
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21364}=\sqrt{196*109}=\sqrt{196}*\sqrt{109}=14\sqrt{109}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-14\sqrt{109}}{2*9}=\frac{130-14\sqrt{109}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+14\sqrt{109}}{2*9}=\frac{130+14\sqrt{109}}{18} $
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