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(x+85)(x+40)/2=2160
We move all terms to the left:
(x+85)(x+40)/2-(2160)=0
We multiply parentheses ..
(+x^2+40x+85x+3400)/2-2160=0
We multiply all the terms by the denominator
(+x^2+40x+85x+3400)-2160*2=0
We add all the numbers together, and all the variables
(+x^2+40x+85x+3400)-4320=0
We get rid of parentheses
x^2+40x+85x+3400-4320=0
We add all the numbers together, and all the variables
x^2+125x-920=0
a = 1; b = 125; c = -920;
Δ = b2-4ac
Δ = 1252-4·1·(-920)
Δ = 19305
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19305}=\sqrt{9*2145}=\sqrt{9}*\sqrt{2145}=3\sqrt{2145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-3\sqrt{2145}}{2*1}=\frac{-125-3\sqrt{2145}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+3\sqrt{2145}}{2*1}=\frac{-125+3\sqrt{2145}}{2} $
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