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(240+x)(375+x)=171.000
We move all terms to the left:
(240+x)(375+x)-(171.000)=0
We add all the numbers together, and all the variables
(x+240)(x+375)-171=0
We multiply parentheses ..
(+x^2+375x+240x+90000)-171=0
We get rid of parentheses
x^2+375x+240x+90000-171=0
We add all the numbers together, and all the variables
x^2+615x+89829=0
a = 1; b = 615; c = +89829;
Δ = b2-4ac
Δ = 6152-4·1·89829
Δ = 18909
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18909}=\sqrt{9*2101}=\sqrt{9}*\sqrt{2101}=3\sqrt{2101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(615)-3\sqrt{2101}}{2*1}=\frac{-615-3\sqrt{2101}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(615)+3\sqrt{2101}}{2*1}=\frac{-615+3\sqrt{2101}}{2} $
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