14x^2-21=43x

Solution for 14x^2-21=43x equation:

14x^2-21=43x

We move all terms to the left:

14x^2-21-(43x)=0

a = 14; b = -43; c = -21;
Δ = b2-4ac
Δ = -432-4·14·(-21)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-55}{2*14}=\frac{-12}{28}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+55}{2*14}=\frac{98}{28}
=3+1/2
$