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(11x-6)(7x)=180
We move all terms to the left:
(11x-6)(7x)-(180)=0
We multiply parentheses
77x^2-42x-180=0
a = 77; b = -42; c = -180;
Δ = b2-4ac
Δ = -422-4·77·(-180)
Δ = 57204
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{57204}=\sqrt{36*1589}=\sqrt{36}*\sqrt{1589}=6\sqrt{1589}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{1589}}{2*77}=\frac{42-6\sqrt{1589}}{154} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{1589}}{2*77}=\frac{42+6\sqrt{1589}}{154} $
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