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(2x+5)(3x-11)=0
We multiply parentheses ..
(+6x^2-22x+15x-55)=0
We get rid of parentheses
6x^2-22x+15x-55=0
We add all the numbers together, and all the variables
6x^2-7x-55=0
a = 6; b = -7; c = -55;
Δ = b2-4ac
Δ = -72-4·6·(-55)
Δ = 1369
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{1369}=37$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-37}{2*6}=\frac{-30}{12} =-2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+37}{2*6}=\frac{44}{12} =3+2/3 $
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