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22.5x^2-50x=360
We move all terms to the left:
22.5x^2-50x-(360)=0
a = 22.5; b = -50; c = -360;
Δ = b2-4ac
Δ = -502-4·22.5·(-360)
Δ = 34900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34900}=\sqrt{100*349}=\sqrt{100}*\sqrt{349}=10\sqrt{349}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{349}}{2*22.5}=\frac{50-10\sqrt{349}}{45} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{349}}{2*22.5}=\frac{50+10\sqrt{349}}{45} $
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