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.9x(x-20)=830
We move all terms to the left:
.9x(x-20)-(830)=0
We multiply parentheses
x^2-20x-830=0
a = 1; b = -20; c = -830;
Δ = b2-4ac
Δ = -202-4·1·(-830)
Δ = 3720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{930}}{2*1}=\frac{20-2\sqrt{930}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{930}}{2*1}=\frac{20+2\sqrt{930}}{2} $
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