X2+3=6x-5

Solution for X2+3=6x-5 equation:

X2+3=6X-5

We move all terms to the left:

X2+3-(6X-5)=0

We add all the numbers together, and all the variables

X^2-(6X-5)+3=0

We get rid of parentheses

X^2-6X+5+3=0

We add all the numbers together, and all the variables

X^2-6X+8=0

a = 1; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·1·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*1}=\frac{4}{2}
=2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*1}=\frac{8}{2}
=4
$