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4x+8x^2=1.5
We move all terms to the left:
4x+8x^2-(1.5)=0
We add all the numbers together, and all the variables
8x^2+4x-1.5=0
a = 8; b = 4; c = -1.5;
Δ = b2-4ac
Δ = 42-4·8·(-1.5)
Δ = 64
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*8}=\frac{-12}{16} =-3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*8}=\frac{4}{16} =1/4 $
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