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(4x-23)3x=180
We move all terms to the left:
(4x-23)3x-(180)=0
We multiply parentheses
12x^2-69x-180=0
a = 12; b = -69; c = -180;
Δ = b2-4ac
Δ = -692-4·12·(-180)
Δ = 13401
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13401}=\sqrt{9*1489}=\sqrt{9}*\sqrt{1489}=3\sqrt{1489}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-3\sqrt{1489}}{2*12}=\frac{69-3\sqrt{1489}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+3\sqrt{1489}}{2*12}=\frac{69+3\sqrt{1489}}{24} $
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