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150=-6x^2+100x-180
We move all terms to the left:
150-(-6x^2+100x-180)=0
We get rid of parentheses
6x^2-100x+180+150=0
We add all the numbers together, and all the variables
6x^2-100x+330=0
a = 6; b = -100; c = +330;
Δ = b2-4ac
Δ = -1002-4·6·330
Δ = 2080
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{130}}{2*6}=\frac{100-4\sqrt{130}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{130}}{2*6}=\frac{100+4\sqrt{130}}{12} $
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