(2x+5)(x-1)=6x

Solution for (2x+5)(x-1)=6x equation:

(2x+5)(x-1)=6x

We move all terms to the left:

(2x+5)(x-1)-(6x)=0

We add all the numbers together, and all the variables

-6x+(2x+5)(x-1)=0

We multiply parentheses ..

(+2x^2-2x+5x-5)-6x=0

We get rid of parentheses

2x^2-2x+5x-6x-5=0

We add all the numbers together, and all the variables

2x^2-3x-5=0

a = 2; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·2·(-5)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*2}=\frac{10}{4}
=2+1/2
$