(3-14x)(63-9x)=180

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Solution for (3-14x)(63-9x)=180 equation:



(3-14x)(63-9x)=180
We move all terms to the left:
(3-14x)(63-9x)-(180)=0
We add all the numbers together, and all the variables
(-14x+3)(-9x+63)-180=0
We multiply parentheses ..
(+126x^2-882x-27x+189)-180=0
We get rid of parentheses
126x^2-882x-27x+189-180=0
We add all the numbers together, and all the variables
126x^2-909x+9=0
a = 126; b = -909; c = +9;
Δ = b2-4ac
Δ = -9092-4·126·9
Δ = 821745
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:
$\sqrt{\Delta}=\sqrt{821745}=\sqrt{81*10145}=\sqrt{81}*\sqrt{10145}=9\sqrt{10145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-909)-9\sqrt{10145}}{2*126}=\frac{909-9\sqrt{10145}}{252} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-909)+9\sqrt{10145}}{2*126}=\frac{909+9\sqrt{10145}}{252} $

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