2-3x(2x+5)=(x-1)

Solution for 2-3x(2x+5)=(x-1) equation:

2-3x(2x+5)=(x-1)

We move all terms to the left:

2-3x(2x+5)-((x-1))=0

We multiply parentheses

-6x^2-15x-((x-1))+2=0


We calculate terms in parentheses: -((x-1)), so:

(x-1)

We get rid of parentheses

x-1

Back to the equation:

-(x-1)


We get rid of parentheses

-6x^2-15x-x+1+2=0

We add all the numbers together, and all the variables

-6x^2-16x+3=0

a = -6; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·(-6)·3
Δ = 328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{82}}{2*-6}=\frac{16-2\sqrt{82}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{82}}{2*-6}=\frac{16+2\sqrt{82}}{-12}
$