x(2x-5)=150

Solution for x(2x-5)=150 equation:

x(2x-5)=150

We move all terms to the left:

x(2x-5)-(150)=0

We multiply parentheses

2x^2-5x-150=0

a = 2; b = -5; c = -150;
Δ = b2-4ac
Δ = -52-4·2·(-150)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-35}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+35}{2*2}=\frac{40}{4}
=10
$