6x^2+13x-5=(2x+5)

Solution for 6x^2+13x-5=(2x+5) equation:

6x^2+13x-5=(2x+5)

We move all terms to the left:

6x^2+13x-5-((2x+5))=0


We calculate terms in parentheses: -((2x+5)), so:

(2x+5)

We get rid of parentheses

2x+5

Back to the equation:

-(2x+5)


We get rid of parentheses

6x^2+13x-2x-5-5=0

We add all the numbers together, and all the variables

6x^2+11x-10=0

a = 6; b = 11; c = -10;
Δ = b2-4ac
Δ = 112-4·6·(-10)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*6}=\frac{8}{12}
=2/3
$