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6x(2x-7)=5x
We move all terms to the left:
6x(2x-7)-(5x)=0
We add all the numbers together, and all the variables
-5x+6x(2x-7)=0
We multiply parentheses
12x^2-5x-42x=0
We add all the numbers together, and all the variables
12x^2-47x=0
a = 12; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·12·0
Δ = 2209
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{2209}=47$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*12}=\frac{0}{24} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*12}=\frac{94}{24} =3+11/12 $
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