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3x(4x-5)=12x-15
We move all terms to the left:
3x(4x-5)-(12x-15)=0
We multiply parentheses
12x^2-15x-(12x-15)=0
We get rid of parentheses
12x^2-15x-12x+15=0
We add all the numbers together, and all the variables
12x^2-27x+15=0
a = 12; b = -27; c = +15;
Δ = b2-4ac
Δ = -272-4·12·15
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*12}=\frac{24}{24} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*12}=\frac{30}{24} =1+1/4 $
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