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4x^2+120x=-380
We move all terms to the left:
4x^2+120x-(-380)=0
We add all the numbers together, and all the variables
4x^2+120x+380=0
a = 4; b = 120; c = +380;
Δ = b2-4ac
Δ = 1202-4·4·380
Δ = 8320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8320}=\sqrt{64*130}=\sqrt{64}*\sqrt{130}=8\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{130}}{2*4}=\frac{-120-8\sqrt{130}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{130}}{2*4}=\frac{-120+8\sqrt{130}}{8} $
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