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2x(2x-1)+5x=29
We move all terms to the left:
2x(2x-1)+5x-(29)=0
We add all the numbers together, and all the variables
5x+2x(2x-1)-29=0
We multiply parentheses
4x^2+5x-2x-29=0
We add all the numbers together, and all the variables
4x^2+3x-29=0
a = 4; b = 3; c = -29;
Δ = b2-4ac
Δ = 32-4·4·(-29)
Δ = 473
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{-(3)-\sqrt{473}}{2*4}=\frac{-3-\sqrt{473}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{473}}{2*4}=\frac{-3+\sqrt{473}}{8} $
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