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5x+2x(x+10)=83
We move all terms to the left:
5x+2x(x+10)-(83)=0
We multiply parentheses
2x^2+5x+20x-83=0
We add all the numbers together, and all the variables
2x^2+25x-83=0
a = 2; b = 25; c = -83;
Δ = b2-4ac
Δ = 252-4·2·(-83)
Δ = 1289
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{1289}}{2*2}=\frac{-25-\sqrt{1289}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{1289}}{2*2}=\frac{-25+\sqrt{1289}}{4} $
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