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2x(3-2x)=5x-12
We move all terms to the left:
2x(3-2x)-(5x-12)=0
We add all the numbers together, and all the variables
2x(-2x+3)-(5x-12)=0
We multiply parentheses
-4x^2+6x-(5x-12)=0
We get rid of parentheses
-4x^2+6x-5x+12=0
We add all the numbers together, and all the variables
-4x^2+x+12=0
a = -4; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-4)·12
Δ = 193
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)-\sqrt{193}}{2*-4}=\frac{-1-\sqrt{193}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*-4}=\frac{-1+\sqrt{193}}{-8} $
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