x(2x-3)=350

Solution for x(2x-3)=350 equation:

x(2x-3)=350

We move all terms to the left:

x(2x-3)-(350)=0

We multiply parentheses

2x^2-3x-350=0

a = 2; b = -3; c = -350;
Δ = b2-4ac
Δ = -32-4·2·(-350)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-53}{2*2}=\frac{-50}{4}
=-12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+53}{2*2}=\frac{56}{4}
=14
$