6x^2-3x+4=8x+1

Solution for 6x^2-3x+4=8x+1 equation:

6x^2-3x+4=8x+1

We move all terms to the left:

6x^2-3x+4-(8x+1)=0

We get rid of parentheses

6x^2-3x-8x-1+4=0

We add all the numbers together, and all the variables

6x^2-11x+3=0

a = 6; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·6·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*6}=\frac{4}{12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*6}=\frac{18}{12}
=1+1/2
$