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0.5(4x+1)(2x+1)=13
We move all terms to the left:
0.5(4x+1)(2x+1)-(13)=0
We multiply parentheses ..
0.5(+8x^2+4x+2x+1)-13=0
We multiply parentheses
4x^2+2x+x+0.5-13=0
We add all the numbers together, and all the variables
4x^2+3x-12.5=0
a = 4; b = 3; c = -12.5;
Δ = b2-4ac
Δ = 32-4·4·(-12.5)
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{-(3)-\sqrt{209}}{2*4}=\frac{-3-\sqrt{209}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{209}}{2*4}=\frac{-3+\sqrt{209}}{8} $
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