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(4x+1)(x+1)=130
We move all terms to the left:
(4x+1)(x+1)-(130)=0
We multiply parentheses ..
(+4x^2+4x+x+1)-130=0
We get rid of parentheses
4x^2+4x+x+1-130=0
We add all the numbers together, and all the variables
4x^2+5x-129=0
a = 4; b = 5; c = -129;
Δ = b2-4ac
Δ = 52-4·4·(-129)
Δ = 2089
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{-(5)-\sqrt{2089}}{2*4}=\frac{-5-\sqrt{2089}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{2089}}{2*4}=\frac{-5+\sqrt{2089}}{8} $
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