-57x+27=14x^2

Solution for -57x+27=14x^2 equation:

-57x+27=14x^2

We move all terms to the left:

-57x+27-(14x^2)=0

determiningTheFunctionDomain
-14x^2-57x+27=0

a = -14; b = -57; c = +27;
Δ = b2-4ac
Δ = -572-4·(-14)·27
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-69}{2*-14}=\frac{-12}{-28}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+69}{2*-14}=\frac{126}{-28}
=-4+1/2
$