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-2x(2x+3)+3x=-2
We move all terms to the left:
-2x(2x+3)+3x-(-2)=0
We add all the numbers together, and all the variables
3x-2x(2x+3)+2=0
We multiply parentheses
-4x^2+3x-6x+2=0
We add all the numbers together, and all the variables
-4x^2-3x+2=0
a = -4; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-4)·2
Δ = 41
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{-(-3)-\sqrt{41}}{2*-4}=\frac{3-\sqrt{41}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*-4}=\frac{3+\sqrt{41}}{-8} $
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