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(4x+30)(x+5x)=500
We move all terms to the left:
(4x+30)(x+5x)-(500)=0
We add all the numbers together, and all the variables
(4x+30)(+6x)-500=0
We multiply parentheses ..
(+24x^2+180x)-500=0
We get rid of parentheses
24x^2+180x-500=0
a = 24; b = 180; c = -500;
Δ = b2-4ac
Δ = 1802-4·24·(-500)
Δ = 80400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80400}=\sqrt{400*201}=\sqrt{400}*\sqrt{201}=20\sqrt{201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-20\sqrt{201}}{2*24}=\frac{-180-20\sqrt{201}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+20\sqrt{201}}{2*24}=\frac{-180+20\sqrt{201}}{48} $
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