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(2x-8)(3x-10)=17
We move all terms to the left:
(2x-8)(3x-10)-(17)=0
We multiply parentheses ..
(+6x^2-20x-24x+80)-17=0
We get rid of parentheses
6x^2-20x-24x+80-17=0
We add all the numbers together, and all the variables
6x^2-44x+63=0
a = 6; b = -44; c = +63;
Δ = b2-4ac
Δ = -442-4·6·63
Δ = 424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{106}}{2*6}=\frac{44-2\sqrt{106}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{106}}{2*6}=\frac{44+2\sqrt{106}}{12} $
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