5x^2=7+5x

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Solution for 5x^2=7+5x equation:



5x^2=7+5x
We move all terms to the left:
5x^2-(7+5x)=0
We add all the numbers together, and all the variables
5x^2-(5x+7)=0
We get rid of parentheses
5x^2-5x-7=0
a = 5; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·5·(-7)
Δ = 165
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{-(-5)-\sqrt{165}}{2*5}=\frac{5-\sqrt{165}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{165}}{2*5}=\frac{5+\sqrt{165}}{10} $

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