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(x-12)7x=180
We move all terms to the left:
(x-12)7x-(180)=0
We multiply parentheses
7x^2-84x-180=0
a = 7; b = -84; c = -180;
Δ = b2-4ac
Δ = -842-4·7·(-180)
Δ = 12096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-24\sqrt{21}}{2*7}=\frac{84-24\sqrt{21}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+24\sqrt{21}}{2*7}=\frac{84+24\sqrt{21}}{14} $
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