x^2=(6x-5)

Solution for x^2=(6x-5) equation:

x^2=(6x-5)

We move all terms to the left:

x^2-((6x-5))=0


We calculate terms in parentheses: -((6x-5)), so:

(6x-5)

We get rid of parentheses

6x-5

Back to the equation:

-(6x-5)


We get rid of parentheses

x^2-6x+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$