35x=-16x+2x^2

Solution for 35x=-16x+2x^2 equation:

35x=-16x+2x^2

We move all terms to the left:

35x-(-16x+2x^2)=0

We get rid of parentheses

-2x^2+16x+35x=0

We add all the numbers together, and all the variables

-2x^2+51x=0

a = -2; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-2)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-2}=\frac{-102}{-4}
=25+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-2}=\frac{0}{-4}
=0
$