x(4x-6)=340

Solution for x(4x-6)=340 equation:

x(4x-6)=340

We move all terms to the left:

x(4x-6)-(340)=0

We multiply parentheses

4x^2-6x-340=0

a = 4; b = -6; c = -340;
Δ = b2-4ac
Δ = -62-4·4·(-340)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-74}{2*4}=\frac{-68}{8}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+74}{2*4}=\frac{80}{8}
=10
$