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.50x+.40x(700-x)=310
We move all terms to the left:
.50x+.40x(700-x)-(310)=0
We add all the numbers together, and all the variables
.50x+.40x(-1x+700)-310=0
We multiply parentheses
-1x^2+.50x+700x-310=0
We add all the numbers together, and all the variables
-1x^2+700.5x-310=0
a = -1; b = 700.5; c = -310;
Δ = b2-4ac
Δ = 700.52-4·(-1)·(-310)
Δ = 489460.25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700.5)-\sqrt{489460.25}}{2*-1}=\frac{-700.5-\sqrt{489460.25}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700.5)+\sqrt{489460.25}}{2*-1}=\frac{-700.5+\sqrt{489460.25}}{-2} $
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