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x+5x(35+x)=385
We move all terms to the left:
x+5x(35+x)-(385)=0
We add all the numbers together, and all the variables
x+5x(x+35)-385=0
We multiply parentheses
5x^2+x+175x-385=0
We add all the numbers together, and all the variables
5x^2+176x-385=0
a = 5; b = 176; c = -385;
Δ = b2-4ac
Δ = 1762-4·5·(-385)
Δ = 38676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{38676}=\sqrt{4*9669}=\sqrt{4}*\sqrt{9669}=2\sqrt{9669}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-2\sqrt{9669}}{2*5}=\frac{-176-2\sqrt{9669}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+2\sqrt{9669}}{2*5}=\frac{-176+2\sqrt{9669}}{10} $
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