6x+5=5x^2

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Solution for 6x+5=5x^2 equation:



6x+5=5x^2
We move all terms to the left:
6x+5-(5x^2)=0
determiningTheFunctionDomain -5x^2+6x+5=0
a = -5; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-5)·5
Δ = 136
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:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{34}}{2*-5}=\frac{-6-2\sqrt{34}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{34}}{2*-5}=\frac{-6+2\sqrt{34}}{-10} $

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