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6.50x+2x(10+x)=4x
We move all terms to the left:
6.50x+2x(10+x)-(4x)=0
We add all the numbers together, and all the variables
6.50x+2x(x+10)-4x=0
We add all the numbers together, and all the variables
2.5x+2x(x+10)=0
We multiply parentheses
2x^2+2.5x+20x=0
We add all the numbers together, and all the variables
2x^2+22.5x=0
a = 2; b = 22.5; c = 0;
Δ = b2-4ac
Δ = 22.52-4·2·0
Δ = 506.25
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{-(22.5)-\sqrt{506.25}}{2*2}=\frac{-22.5-\sqrt{506.25}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22.5)+\sqrt{506.25}}{2*2}=\frac{-22.5+\sqrt{506.25}}{4} $
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