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12x(4x+10)=7x
We move all terms to the left:
12x(4x+10)-(7x)=0
We add all the numbers together, and all the variables
-7x+12x(4x+10)=0
We multiply parentheses
48x^2-7x+120x=0
We add all the numbers together, and all the variables
48x^2+113x=0
a = 48; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·48·0
Δ = 12769
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{12769}=113$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*48}=\frac{-226}{96} =-2+17/48 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*48}=\frac{0}{96} =0 $
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