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(11x+17)(2x-13)=0
We multiply parentheses ..
(+22x^2-143x+34x-221)=0
We get rid of parentheses
22x^2-143x+34x-221=0
We add all the numbers together, and all the variables
22x^2-109x-221=0
a = 22; b = -109; c = -221;
Δ = b2-4ac
Δ = -1092-4·22·(-221)
Δ = 31329
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{31329}=177$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-177}{2*22}=\frac{-68}{44} =-1+6/11 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+177}{2*22}=\frac{286}{44} =6+1/2 $
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