(5x-32)(7x+56)=90

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Solution for (5x-32)(7x+56)=90 equation:



(5x-32)(7x+56)=90
We move all terms to the left:
(5x-32)(7x+56)-(90)=0
We multiply parentheses ..
(+35x^2+280x-224x-1792)-90=0
We get rid of parentheses
35x^2+280x-224x-1792-90=0
We add all the numbers together, and all the variables
35x^2+56x-1882=0
a = 35; b = 56; c = -1882;
Δ = b2-4ac
Δ = 562-4·35·(-1882)
Δ = 266616
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:
$\sqrt{\Delta}=\sqrt{266616}=\sqrt{19044*14}=\sqrt{19044}*\sqrt{14}=138\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-138\sqrt{14}}{2*35}=\frac{-56-138\sqrt{14}}{70} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+138\sqrt{14}}{2*35}=\frac{-56+138\sqrt{14}}{70} $

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