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6.50x+2x(10+x)=4
We move all terms to the left:
6.50x+2x(10+x)-(4)=0
We add all the numbers together, and all the variables
6.50x+2x(x+10)-4=0
We multiply parentheses
2x^2+6.50x+20x-4=0
We add all the numbers together, and all the variables
2x^2+26.5x-4=0
a = 2; b = 26.5; c = -4;
Δ = b2-4ac
Δ = 26.52-4·2·(-4)
Δ = 734.25
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{-(26.5)-\sqrt{734.25}}{2*2}=\frac{-26.5-\sqrt{734.25}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26.5)+\sqrt{734.25}}{2*2}=\frac{-26.5+\sqrt{734.25}}{4} $
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