(2x+5)(3x-2)-1=10x

Solution for (2x+5)(3x-2)-1=10x equation:

(2x+5)(3x-2)-1=10x

We move all terms to the left:

(2x+5)(3x-2)-1-(10x)=0

We add all the numbers together, and all the variables

-10x+(2x+5)(3x-2)-1=0

We multiply parentheses ..

(+6x^2-4x+15x-10)-10x-1=0

We get rid of parentheses

6x^2-4x+15x-10x-10-1=0

We add all the numbers together, and all the variables

6x^2+x-11=0

a = 6; b = 1; c = -11;
Δ = b2-4ac
Δ = 12-4·6·(-11)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{265}}{2*6}=\frac{-1-\sqrt{265}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{265}}{2*6}=\frac{-1+\sqrt{265}}{12}
$