x(2x-5)=375

Solution for x(2x-5)=375 equation:

x(2x-5)=375

We move all terms to the left:

x(2x-5)-(375)=0

We multiply parentheses

2x^2-5x-375=0

a = 2; b = -5; c = -375;
Δ = b2-4ac
Δ = -52-4·2·(-375)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-55}{2*2}=\frac{-50}{4}
=-12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+55}{2*2}=\frac{60}{4}
=15
$