X(2x-14)=144

Solution for X(2x-14)=144 equation:

X(2X-14)=144

We move all terms to the left:

X(2X-14)-(144)=0

We multiply parentheses

2X^2-14X-144=0

a = 2; b = -14; c = -144;
Δ = b2-4ac
Δ = -142-4·2·(-144)
Δ = 1348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1348}=\sqrt{4*337}=\sqrt{4}*\sqrt{337}=2\sqrt{337}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{337}}{2*2}=\frac{14-2\sqrt{337}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{337}}{2*2}=\frac{14+2\sqrt{337}}{4}
$