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4x(x-3)=61x
We move all terms to the left:
4x(x-3)-(61x)=0
We add all the numbers together, and all the variables
-61x+4x(x-3)=0
We multiply parentheses
4x^2-61x-12x=0
We add all the numbers together, and all the variables
4x^2-73x=0
a = 4; b = -73; c = 0;
Δ = b2-4ac
Δ = -732-4·4·0
Δ = 5329
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{5329}=73$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-73}{2*4}=\frac{0}{8} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+73}{2*4}=\frac{146}{8} =18+1/4 $
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