x2=7x+4

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Solution for x2=7x+4 equation:



x2=7x+4
We move all terms to the left:
x2-(7x+4)=0
We add all the numbers together, and all the variables
x^2-(7x+4)=0
We get rid of parentheses
x^2-7x-4=0
a = 1; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·1·(-4)
Δ = 65
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{-(-7)-\sqrt{65}}{2*1}=\frac{7-\sqrt{65}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{65}}{2*1}=\frac{7+\sqrt{65}}{2} $

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