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130x-(2800+6x+0.1x^2)=0
We get rid of parentheses
-0.1x^2-6x+130x-2800=0
We add all the numbers together, and all the variables
-0.1x^2+124x-2800=0
a = -0.1; b = 124; c = -2800;
Δ = b2-4ac
Δ = 1242-4·(-0.1)·(-2800)
Δ = 14256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14256}=\sqrt{1296*11}=\sqrt{1296}*\sqrt{11}=36\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-36\sqrt{11}}{2*-0.1}=\frac{-124-36\sqrt{11}}{-0.2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+36\sqrt{11}}{2*-0.1}=\frac{-124+36\sqrt{11}}{-0.2} $
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