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4.5x(x+4)=6.5x
We move all terms to the left:
4.5x(x+4)-(6.5x)=0
We add all the numbers together, and all the variables
4.5x(x+4)-(+6.5x)=0
We multiply parentheses
4x^2+16x-(+6.5x)=0
We get rid of parentheses
4x^2+16x-6.5x=0
We add all the numbers together, and all the variables
4x^2+9.5x=0
a = 4; b = 9.5; c = 0;
Δ = b2-4ac
Δ = 9.52-4·4·0
Δ = 90.25
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{-(9.5)-\sqrt{90.25}}{2*4}=\frac{-9.5-\sqrt{90.25}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.5)+\sqrt{90.25}}{2*4}=\frac{-9.5+\sqrt{90.25}}{8} $
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