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(4x-1)(12x-17)=48
We move all terms to the left:
(4x-1)(12x-17)-(48)=0
We multiply parentheses ..
(+48x^2-68x-12x+17)-48=0
We get rid of parentheses
48x^2-68x-12x+17-48=0
We add all the numbers together, and all the variables
48x^2-80x-31=0
a = 48; b = -80; c = -31;
Δ = b2-4ac
Δ = -802-4·48·(-31)
Δ = 12352
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12352}=\sqrt{64*193}=\sqrt{64}*\sqrt{193}=8\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{193}}{2*48}=\frac{80-8\sqrt{193}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{193}}{2*48}=\frac{80+8\sqrt{193}}{96} $
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