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(8x-17)(5x+13)=0
We multiply parentheses ..
(+40x^2+104x-85x-221)=0
We get rid of parentheses
40x^2+104x-85x-221=0
We add all the numbers together, and all the variables
40x^2+19x-221=0
a = 40; b = 19; c = -221;
Δ = b2-4ac
Δ = 192-4·40·(-221)
Δ = 35721
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{35721}=189$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-189}{2*40}=\frac{-208}{80} =-2+3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+189}{2*40}=\frac{170}{80} =2+1/8 $
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