5x(-2x+5)+x-5=-43

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Solution for 5x(-2x+5)+x-5=-43 equation:



5x(-2x+5)+x-5=-43
We move all terms to the left:
5x(-2x+5)+x-5-(-43)=0
We add all the numbers together, and all the variables
x+5x(-2x+5)+38=0
We multiply parentheses
-10x^2+x+25x+38=0
We add all the numbers together, and all the variables
-10x^2+26x+38=0
a = -10; b = 26; c = +38;
Δ = b2-4ac
Δ = 262-4·(-10)·38
Δ = 2196
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:
$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6\sqrt{61}}{2*-10}=\frac{-26-6\sqrt{61}}{-20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6\sqrt{61}}{2*-10}=\frac{-26+6\sqrt{61}}{-20} $

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