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10(4x)=3x(x-3)
We move all terms to the left:
10(4x)-(3x(x-3))=0
We calculate terms in parentheses: -(3x(x-3)), so:We get rid of parentheses
3x(x-3)
We multiply parentheses
3x^2-9x
Back to the equation:
-(3x^2-9x)
-3x^2+104x+9x=0
We add all the numbers together, and all the variables
-3x^2+113x=0
a = -3; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·(-3)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*-3}=\frac{-226}{-6} =37+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*-3}=\frac{0}{-6} =0 $
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