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3x^2=118.5x-338
We move all terms to the left:
3x^2-(118.5x-338)=0
We get rid of parentheses
3x^2-118.5x+338=0
a = 3; b = -118.5; c = +338;
Δ = b2-4ac
Δ = -118.52-4·3·338
Δ = 9986.25
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{-(-118.5)-\sqrt{9986.25}}{2*3}=\frac{118.5-\sqrt{9986.25}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118.5)+\sqrt{9986.25}}{2*3}=\frac{118.5+\sqrt{9986.25}}{6} $
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