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(2x-20)(5x+10)=2.9
We move all terms to the left:
(2x-20)(5x+10)-(2.9)=0
We add all the numbers together, and all the variables
(2x-20)(5x+10)-2.9=0
We multiply parentheses ..
(+10x^2+20x-100x-200)-2.9=0
We get rid of parentheses
10x^2+20x-100x-200-2.9=0
We add all the numbers together, and all the variables
10x^2-80x-202.9=0
a = 10; b = -80; c = -202.9;
Δ = b2-4ac
Δ = -802-4·10·(-202.9)
Δ = 14516
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14516}=\sqrt{4*3629}=\sqrt{4}*\sqrt{3629}=2\sqrt{3629}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{3629}}{2*10}=\frac{80-2\sqrt{3629}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{3629}}{2*10}=\frac{80+2\sqrt{3629}}{20} $
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