-5(2+x)x=7x-4

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Solution for -5(2+x)x=7x-4 equation:



-5(2+x)x=7x-4
We move all terms to the left:
-5(2+x)x-(7x-4)=0
We add all the numbers together, and all the variables
-5(x+2)x-(7x-4)=0
We multiply parentheses
-5x^2-10x-(7x-4)=0
We get rid of parentheses
-5x^2-10x-7x+4=0
We add all the numbers together, and all the variables
-5x^2-17x+4=0
a = -5; b = -17; c = +4;
Δ = b2-4ac
Δ = -172-4·(-5)·4
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{41}}{2*-5}=\frac{17-3\sqrt{41}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{41}}{2*-5}=\frac{17+3\sqrt{41}}{-10} $

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