(2x)(5x-2)/2=115

Solution for (2x)(5x-2)/2=115 equation:

(2x)(5x-2)/2=115

We move all terms to the left:

(2x)(5x-2)/2-(115)=0

We multiply all the terms by the denominator


2x(5x-2)-115*2=0

We add all the numbers together, and all the variables

2x(5x-2)-230=0

We multiply parentheses

10x^2-4x-230=0

a = 10; b = -4; c = -230;
Δ = b2-4ac
Δ = -42-4·10·(-230)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-96}{2*10}=\frac{-92}{20}
=-4+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+96}{2*10}=\frac{100}{20}
=5
$