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0=312.5x^2-50x-1.5
We move all terms to the left:
0-(312.5x^2-50x-1.5)=0
We add all the numbers together, and all the variables
-(312.5x^2-50x-1.5)=0
We get rid of parentheses
-312.5x^2+50x+1.5=0
a = -312.5; b = 50; c = +1.5;
Δ = b2-4ac
Δ = 502-4·(-312.5)·1.5
Δ = 4375
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4375}=\sqrt{625*7}=\sqrt{625}*\sqrt{7}=25\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-25\sqrt{7}}{2*-312.5}=\frac{-50-25\sqrt{7}}{-625} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+25\sqrt{7}}{2*-312.5}=\frac{-50+25\sqrt{7}}{-625} $
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