4x^2-144=14x

Solution for 4x^2-144=14x equation:

4x^2-144=14x

We move all terms to the left:

4x^2-144-(14x)=0

a = 4; b = -14; c = -144;
Δ = b2-4ac
Δ = -142-4·4·(-144)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-50}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+50}{2*4}=\frac{64}{8}
=8
$