35-69x=54x^2

Solution for 35-69x=54x^2 equation:

35-69x=54x^2

We move all terms to the left:

35-69x-(54x^2)=0

determiningTheFunctionDomain
-54x^2-69x+35=0

a = -54; b = -69; c = +35;
Δ = b2-4ac
Δ = -692-4·(-54)·35
Δ = 12321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12321}=111$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-111}{2*-54}=\frac{-42}{-108}
=7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+111}{2*-54}=\frac{180}{-108}
=-1+2/3
$