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4x(3x-7)-5(2x-4)=3x
We move all terms to the left:
4x(3x-7)-5(2x-4)-(3x)=0
We add all the numbers together, and all the variables
-3x+4x(3x-7)-5(2x-4)=0
We multiply parentheses
12x^2-3x-28x-10x+20=0
We add all the numbers together, and all the variables
12x^2-41x+20=0
a = 12; b = -41; c = +20;
Δ = b2-4ac
Δ = -412-4·12·20
Δ = 721
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{-(-41)-\sqrt{721}}{2*12}=\frac{41-\sqrt{721}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{721}}{2*12}=\frac{41+\sqrt{721}}{24} $
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