x(2x-3)=68

Solution for x(2x-3)=68 equation:

x(2x-3)=68

We move all terms to the left:

x(2x-3)-(68)=0

We multiply parentheses

2x^2-3x-68=0

a = 2; b = -3; c = -68;
Δ = b2-4ac
Δ = -32-4·2·(-68)
Δ = 553
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{553}}{2*2}=\frac{3-\sqrt{553}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{553}}{2*2}=\frac{3+\sqrt{553}}{4}
$