x(2x-7)=130

Solution for x(2x-7)=130 equation:

x(2x-7)=130

We move all terms to the left:

x(2x-7)-(130)=0

We multiply parentheses

2x^2-7x-130=0

a = 2; b = -7; c = -130;
Δ = b2-4ac
Δ = -72-4·2·(-130)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-33}{2*2}=\frac{-26}{4}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+33}{2*2}=\frac{40}{4}
=10
$