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x(x+8)/2=45
We move all terms to the left:
x(x+8)/2-(45)=0
We multiply all the terms by the denominator
x(x+8)-45*2=0
We add all the numbers together, and all the variables
x(x+8)-90=0
We multiply parentheses
x^2+8x-90=0
a = 1; b = 8; c = -90;
Δ = b2-4ac
Δ = 82-4·1·(-90)
Δ = 424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{106}}{2*1}=\frac{-8-2\sqrt{106}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{106}}{2*1}=\frac{-8+2\sqrt{106}}{2} $
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