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5(x-2)(2x-5)=4x
We move all terms to the left:
5(x-2)(2x-5)-(4x)=0
We add all the numbers together, and all the variables
-4x+5(x-2)(2x-5)=0
We multiply parentheses ..
5(+2x^2-5x-4x+10)-4x=0
We multiply parentheses
10x^2-25x-20x-4x+50=0
We add all the numbers together, and all the variables
10x^2-49x+50=0
a = 10; b = -49; c = +50;
Δ = b2-4ac
Δ = -492-4·10·50
Δ = 401
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{401}}{2*10}=\frac{49-\sqrt{401}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{401}}{2*10}=\frac{49+\sqrt{401}}{20} $
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