35x^2=8-51x

Solution for 35x^2=8-51x equation:

35x^2=8-51x

We move all terms to the left:

35x^2-(8-51x)=0

We add all the numbers together, and all the variables

35x^2-(-51x+8)=0

We get rid of parentheses

35x^2+51x-8=0

a = 35; b = 51; c = -8;
Δ = b2-4ac
Δ = 512-4·35·(-8)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-61}{2*35}=\frac{-112}{70}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+61}{2*35}=\frac{10}{70}
=1/7
$