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14(x-3)22x=-18
We move all terms to the left:
14(x-3)22x-(-18)=0
We add all the numbers together, and all the variables
14(x-3)22x+18=0
We multiply parentheses
308x^2-924x+18=0
a = 308; b = -924; c = +18;
Δ = b2-4ac
Δ = -9242-4·308·18
Δ = 831600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{831600}=\sqrt{3600*231}=\sqrt{3600}*\sqrt{231}=60\sqrt{231}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-924)-60\sqrt{231}}{2*308}=\frac{924-60\sqrt{231}}{616} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-924)+60\sqrt{231}}{2*308}=\frac{924+60\sqrt{231}}{616} $
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