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450=1.5x^2+68x
We move all terms to the left:
450-(1.5x^2+68x)=0
We get rid of parentheses
-1.5x^2-68x+450=0
a = -1.5; b = -68; c = +450;
Δ = b2-4ac
Δ = -682-4·(-1.5)·450
Δ = 7324
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7324}=\sqrt{4*1831}=\sqrt{4}*\sqrt{1831}=2\sqrt{1831}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-2\sqrt{1831}}{2*-1.5}=\frac{68-2\sqrt{1831}}{-3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+2\sqrt{1831}}{2*-1.5}=\frac{68+2\sqrt{1831}}{-3} $
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