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4x^2+80x+384=2.5
We move all terms to the left:
4x^2+80x+384-(2.5)=0
We add all the numbers together, and all the variables
4x^2+80x+381.5=0
a = 4; b = 80; c = +381.5;
Δ = b2-4ac
Δ = 802-4·4·381.5
Δ = 296
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{74}}{2*4}=\frac{-80-2\sqrt{74}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{74}}{2*4}=\frac{-80+2\sqrt{74}}{8} $
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