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(4x-5)(x+1)=8
We move all terms to the left:
(4x-5)(x+1)-(8)=0
We multiply parentheses ..
(+4x^2+4x-5x-5)-8=0
We get rid of parentheses
4x^2+4x-5x-5-8=0
We add all the numbers together, and all the variables
4x^2-1x-13=0
a = 4; b = -1; c = -13;
Δ = b2-4ac
Δ = -12-4·4·(-13)
Δ = 209
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{209}}{2*4}=\frac{1-\sqrt{209}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{209}}{2*4}=\frac{1+\sqrt{209}}{8} $
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