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2.25x^2-25x=1200
We move all terms to the left:
2.25x^2-25x-(1200)=0
a = 2.25; b = -25; c = -1200;
Δ = b2-4ac
Δ = -252-4·2.25·(-1200)
Δ = 11425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11425}=\sqrt{25*457}=\sqrt{25}*\sqrt{457}=5\sqrt{457}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{457}}{2*2.25}=\frac{25-5\sqrt{457}}{4.5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{457}}{2*2.25}=\frac{25+5\sqrt{457}}{4.5} $
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