4x2+x+1=35

Solution for 4x2+x+1=35 equation:

4x^2+x+1=35

We move all terms to the left:

4x^2+x+1-(35)=0

We add all the numbers together, and all the variables

4x^2+x-34=0

a = 4; b = 1; c = -34;
Δ = b2-4ac
Δ = 12-4·4·(-34)
Δ = 545
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{-(1)-\sqrt{545}}{2*4}=\frac{-1-\sqrt{545}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{545}}{2*4}=\frac{-1+\sqrt{545}}{8}
$