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4x(x-5)=4x+5x
We move all terms to the left:
4x(x-5)-(4x+5x)=0
We add all the numbers together, and all the variables
4x(x-5)-(+9x)=0
We multiply parentheses
4x^2-20x-(+9x)=0
We get rid of parentheses
4x^2-20x-9x=0
We add all the numbers together, and all the variables
4x^2-29x=0
a = 4; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·4·0
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*4}=\frac{0}{8} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*4}=\frac{58}{8} =7+1/4 $
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