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20x(x+0.25)+40x=120
We move all terms to the left:
20x(x+0.25)+40x-(120)=0
We add all the numbers together, and all the variables
40x+20x(x+0.25)-120=0
We multiply parentheses
20x^2+40x+5x-120=0
We add all the numbers together, and all the variables
20x^2+45x-120=0
a = 20; b = 45; c = -120;
Δ = b2-4ac
Δ = 452-4·20·(-120)
Δ = 11625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11625}=\sqrt{25*465}=\sqrt{25}*\sqrt{465}=5\sqrt{465}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{465}}{2*20}=\frac{-45-5\sqrt{465}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{465}}{2*20}=\frac{-45+5\sqrt{465}}{40} $
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