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(5x-32)(7x+56)=180
We move all terms to the left:
(5x-32)(7x+56)-(180)=0
We multiply parentheses ..
(+35x^2+280x-224x-1792)-180=0
We get rid of parentheses
35x^2+280x-224x-1792-180=0
We add all the numbers together, and all the variables
35x^2+56x-1972=0
a = 35; b = 56; c = -1972;
Δ = b2-4ac
Δ = 562-4·35·(-1972)
Δ = 279216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{279216}=\sqrt{144*1939}=\sqrt{144}*\sqrt{1939}=12\sqrt{1939}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-12\sqrt{1939}}{2*35}=\frac{-56-12\sqrt{1939}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+12\sqrt{1939}}{2*35}=\frac{-56+12\sqrt{1939}}{70} $
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