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30.25x=10.82x^2-65800x+100000000
We move all terms to the left:
30.25x-(10.82x^2-65800x+100000000)=0
We get rid of parentheses
-10.82x^2+30.25x+65800x-100000000=0
We add all the numbers together, and all the variables
-10.82x^2+65830.25x-100000000=0
a = -10.82; b = 65830.25; c = -100000000;
Δ = b2-4ac
Δ = 65830.252-4·(-10.82)·(-100000000)
Δ = 5621815.0625
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{-(65830.25)-\sqrt{5621815.0625}}{2*-10.82}=\frac{-65830.25-\sqrt{5621815.0625}}{-21.64} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65830.25)+\sqrt{5621815.0625}}{2*-10.82}=\frac{-65830.25+\sqrt{5621815.0625}}{-21.64} $
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