2x^2+6=3x+35

Solution for 2x^2+6=3x+35 equation:

2x^2+6=3x+35

We move all terms to the left:

2x^2+6-(3x+35)=0

We get rid of parentheses

2x^2-3x-35+6=0

We add all the numbers together, and all the variables

2x^2-3x-29=0

a = 2; b = -3; c = -29;
Δ = b2-4ac
Δ = -32-4·2·(-29)
Δ = 241
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{-(-3)-\sqrt{241}}{2*2}=\frac{3-\sqrt{241}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{241}}{2*2}=\frac{3+\sqrt{241}}{4}
$