(2x-6)(x)=154

Solution for (2x-6)(x)=154 equation:

(2x-6)(x)=154

We move all terms to the left:

(2x-6)(x)-(154)=0

We multiply parentheses

2x^2-6x-154=0

a = 2; b = -6; c = -154;
Δ = b2-4ac
Δ = -62-4·2·(-154)
Δ = 1268
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:

$\sqrt{\Delta}=\sqrt{1268}=\sqrt{4*317}=\sqrt{4}*\sqrt{317}=2\sqrt{317}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{317}}{2*2}=\frac{6-2\sqrt{317}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{317}}{2*2}=\frac{6+2\sqrt{317}}{4}
$