2x^2=29x+85

Solution for 2x^2=29x+85 equation:

2x^2=29x+85

We move all terms to the left:

2x^2-(29x+85)=0

We get rid of parentheses

2x^2-29x-85=0

a = 2; b = -29; c = -85;
Δ = b2-4ac
Δ = -292-4·2·(-85)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-39}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+39}{2*2}=\frac{68}{4}
=17
$