34=5x+6x^2

Solution for 34=5x+6x^2 equation:

34=5x+6x^2

We move all terms to the left:

34-(5x+6x^2)=0

We get rid of parentheses

-6x^2-5x+34=0

a = -6; b = -5; c = +34;
Δ = b2-4ac
Δ = -52-4·(-6)·34
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-29}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+29}{2*-6}=\frac{34}{-12}
=-2+5/6
$