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0.4x(5x-12)+0.5x=15.2
We move all terms to the left:
0.4x(5x-12)+0.5x-(15.2)=0
We add all the numbers together, and all the variables
0.5x+0.4x(5x-12)-15.2=0
We multiply parentheses
0x^2+0.5x+0x-15.2=0
We add all the numbers together, and all the variables
x^2+1.5x-15.2=0
a = 1; b = 1.5; c = -15.2;
Δ = b2-4ac
Δ = 1.52-4·1·(-15.2)
Δ = 63.05
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{-(1.5)-\sqrt{63.05}}{2*1}=\frac{-1.5-\sqrt{63.05}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{63.05}}{2*1}=\frac{-1.5+\sqrt{63.05}}{2} $
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