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

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



4x(2x-5)=5x+4
We move all terms to the left:
4x(2x-5)-(5x+4)=0
We multiply parentheses
8x^2-20x-(5x+4)=0
We get rid of parentheses
8x^2-20x-5x-4=0
We add all the numbers together, and all the variables
8x^2-25x-4=0
a = 8; b = -25; c = -4;
Δ = b2-4ac
Δ = -252-4·8·(-4)
Δ = 753
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{-(-25)-\sqrt{753}}{2*8}=\frac{25-\sqrt{753}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{753}}{2*8}=\frac{25+\sqrt{753}}{16} $

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