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4x(2x-3)=-6x+9
We move all terms to the left:
4x(2x-3)-(-6x+9)=0
We multiply parentheses
8x^2-12x-(-6x+9)=0
We get rid of parentheses
8x^2-12x+6x-9=0
We add all the numbers together, and all the variables
8x^2-6x-9=0
a = 8; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·8·(-9)
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*8}=\frac{-12}{16} =-3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*8}=\frac{24}{16} =1+1/2 $
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