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5990=-10x^2+475x+3500
We move all terms to the left:
5990-(-10x^2+475x+3500)=0
We get rid of parentheses
10x^2-475x-3500+5990=0
We add all the numbers together, and all the variables
10x^2-475x+2490=0
a = 10; b = -475; c = +2490;
Δ = b2-4ac
Δ = -4752-4·10·2490
Δ = 126025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{126025}=355$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-475)-355}{2*10}=\frac{120}{20} =6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-475)+355}{2*10}=\frac{830}{20} =41+1/2 $
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