2x(x-5)=5x-4

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Solution for 2x(x-5)=5x-4 equation:



2x(x-5)=5x-4
We move all terms to the left:
2x(x-5)-(5x-4)=0
We multiply parentheses
2x^2-10x-(5x-4)=0
We get rid of parentheses
2x^2-10x-5x+4=0
We add all the numbers together, and all the variables
2x^2-15x+4=0
a = 2; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·2·4
Δ = 193
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{-(-15)-\sqrt{193}}{2*2}=\frac{15-\sqrt{193}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{193}}{2*2}=\frac{15+\sqrt{193}}{4} $

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