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(5x+50)(10x+90)=55
We move all terms to the left:
(5x+50)(10x+90)-(55)=0
We multiply parentheses ..
(+50x^2+450x+500x+4500)-55=0
We get rid of parentheses
50x^2+450x+500x+4500-55=0
We add all the numbers together, and all the variables
50x^2+950x+4445=0
a = 50; b = 950; c = +4445;
Δ = b2-4ac
Δ = 9502-4·50·4445
Δ = 13500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13500}=\sqrt{900*15}=\sqrt{900}*\sqrt{15}=30\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(950)-30\sqrt{15}}{2*50}=\frac{-950-30\sqrt{15}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(950)+30\sqrt{15}}{2*50}=\frac{-950+30\sqrt{15}}{100} $
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