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(4x-11)(8x+19)=0
We multiply parentheses ..
(+32x^2+76x-88x-209)=0
We get rid of parentheses
32x^2+76x-88x-209=0
We add all the numbers together, and all the variables
32x^2-12x-209=0
a = 32; b = -12; c = -209;
Δ = b2-4ac
Δ = -122-4·32·(-209)
Δ = 26896
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{26896}=164$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-164}{2*32}=\frac{-152}{64} =-2+3/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+164}{2*32}=\frac{176}{64} =2+3/4 $
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