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(x+20)(2x+10)=537.5
We move all terms to the left:
(x+20)(2x+10)-(537.5)=0
We add all the numbers together, and all the variables
(x+20)(2x+10)-537.5=0
We multiply parentheses ..
(+2x^2+10x+40x+200)-537.5=0
We get rid of parentheses
2x^2+10x+40x+200-537.5=0
We add all the numbers together, and all the variables
2x^2+50x-337.5=0
a = 2; b = 50; c = -337.5;
Δ = b2-4ac
Δ = 502-4·2·(-337.5)
Δ = 5200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-20\sqrt{13}}{2*2}=\frac{-50-20\sqrt{13}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+20\sqrt{13}}{2*2}=\frac{-50+20\sqrt{13}}{4} $
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