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(8x-19)(5x+11)=0
We multiply parentheses ..
(+40x^2+88x-95x-209)=0
We get rid of parentheses
40x^2+88x-95x-209=0
We add all the numbers together, and all the variables
40x^2-7x-209=0
a = 40; b = -7; c = -209;
Δ = b2-4ac
Δ = -72-4·40·(-209)
Δ = 33489
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{33489}=183$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-183}{2*40}=\frac{-176}{80} =-2+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+183}{2*40}=\frac{190}{80} =2+3/8 $
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