(5x-17)(7x-3)=56

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Solution for (5x-17)(7x-3)=56 equation:



(5x-17)(7x-3)=56
We move all terms to the left:
(5x-17)(7x-3)-(56)=0
We multiply parentheses ..
(+35x^2-15x-119x+51)-56=0
We get rid of parentheses
35x^2-15x-119x+51-56=0
We add all the numbers together, and all the variables
35x^2-134x-5=0
a = 35; b = -134; c = -5;
Δ = b2-4ac
Δ = -1342-4·35·(-5)
Δ = 18656
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:
$\sqrt{\Delta}=\sqrt{18656}=\sqrt{16*1166}=\sqrt{16}*\sqrt{1166}=4\sqrt{1166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134)-4\sqrt{1166}}{2*35}=\frac{134-4\sqrt{1166}}{70} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134)+4\sqrt{1166}}{2*35}=\frac{134+4\sqrt{1166}}{70} $

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