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1.5x+0.5x(x-4)=6
We move all terms to the left:
1.5x+0.5x(x-4)-(6)=0
We multiply parentheses
0x^2+1.5x+0x-6=0
We add all the numbers together, and all the variables
x^2+2.5x-6=0
a = 1; b = 2.5; c = -6;
Δ = b2-4ac
Δ = 2.52-4·1·(-6)
Δ = 30.25
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{-(2.5)-\sqrt{30.25}}{2*1}=\frac{-2.5-\sqrt{30.25}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{30.25}}{2*1}=\frac{-2.5+\sqrt{30.25}}{2} $
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