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.4x(5x-12)+.5x=15.2
We move all terms to the left:
.4x(5x-12)+.5x-(15.2)=0
We add all the numbers together, and all the variables
.5x+.4x(5x-12)-15.2=0
We multiply parentheses
5x^2+.5x-12x-15.2=0
We add all the numbers together, and all the variables
5x^2-11.5x-15.2=0
a = 5; b = -11.5; c = -15.2;
Δ = b2-4ac
Δ = -11.52-4·5·(-15.2)
Δ = 436.25
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{-(-11.5)-\sqrt{436.25}}{2*5}=\frac{11.5-\sqrt{436.25}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.5)+\sqrt{436.25}}{2*5}=\frac{11.5+\sqrt{436.25}}{10} $
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