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3x(7x-20)=108
We move all terms to the left:
3x(7x-20)-(108)=0
We multiply parentheses
21x^2-60x-108=0
a = 21; b = -60; c = -108;
Δ = b2-4ac
Δ = -602-4·21·(-108)
Δ = 12672
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12672}=\sqrt{576*22}=\sqrt{576}*\sqrt{22}=24\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-24\sqrt{22}}{2*21}=\frac{60-24\sqrt{22}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+24\sqrt{22}}{2*21}=\frac{60+24\sqrt{22}}{42} $
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