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0=-0.08x^2+106x-9750
We move all terms to the left:
0-(-0.08x^2+106x-9750)=0
We add all the numbers together, and all the variables
-(-0.08x^2+106x-9750)=0
We get rid of parentheses
0.08x^2-106x+9750=0
a = 0.08; b = -106; c = +9750;
Δ = b2-4ac
Δ = -1062-4·0.08·9750
Δ = 8116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8116}=\sqrt{4*2029}=\sqrt{4}*\sqrt{2029}=2\sqrt{2029}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{2029}}{2*0.08}=\frac{106-2\sqrt{2029}}{0.16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{2029}}{2*0.08}=\frac{106+2\sqrt{2029}}{0.16} $
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