7x-13=(3x+8)(2x-5)

Solution for 7x-13=(3x+8)(2x-5) equation:

7x-13=(3x+8)(2x-5)

We move all terms to the left:

7x-13-((3x+8)(2x-5))=0

We multiply parentheses ..

-((+6x^2-15x+16x-40))+7x-13=0


We calculate terms in parentheses: -((+6x^2-15x+16x-40)), so:

(+6x^2-15x+16x-40)

We get rid of parentheses

6x^2-15x+16x-40

We add all the numbers together, and all the variables

6x^2+x-40

Back to the equation:

-(6x^2+x-40)


We add all the numbers together, and all the variables

7x-(6x^2+x-40)-13=0

We get rid of parentheses

-6x^2+7x-x+40-13=0

We add all the numbers together, and all the variables

-6x^2+6x+27=0

a = -6; b = 6; c = +27;
Δ = b2-4ac
Δ = 62-4·(-6)·27
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{19}}{2*-6}=\frac{-6-6\sqrt{19}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{19}}{2*-6}=\frac{-6+6\sqrt{19}}{-12}
$