X(2x+3)-5=6x

Solution for X(2x+3)-5=6x equation:

X(2X+3)-5=6X

We move all terms to the left:

X(2X+3)-5-(6X)=0

We add all the numbers together, and all the variables

-6X+X(2X+3)-5=0

We multiply parentheses

2X^2-6X+3X-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
$