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(5x-8)(7x+5)=0
We multiply parentheses ..
(+35x^2+25x-56x-40)=0
We get rid of parentheses
35x^2+25x-56x-40=0
We add all the numbers together, and all the variables
35x^2-31x-40=0
a = 35; b = -31; c = -40;
Δ = b2-4ac
Δ = -312-4·35·(-40)
Δ = 6561
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{6561}=81$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-81}{2*35}=\frac{-50}{70} =-5/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+81}{2*35}=\frac{112}{70} =1+3/5 $
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