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10x(8+x)=50
We move all terms to the left:
10x(8+x)-(50)=0
We add all the numbers together, and all the variables
10x(x+8)-50=0
We multiply parentheses
10x^2+80x-50=0
a = 10; b = 80; c = -50;
Δ = b2-4ac
Δ = 802-4·10·(-50)
Δ = 8400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{21}}{2*10}=\frac{-80-20\sqrt{21}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{21}}{2*10}=\frac{-80+20\sqrt{21}}{20} $
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