B=(-2x+5)(7-3x)

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

=(-2B+5)(7-3B)

We move all terms to the left:

-((-2B+5)(7-3B))=0

We add all the numbers together, and all the variables

-((-2B+5)(-3B+7))=0

We multiply parentheses ..

-((+6B^2-14B-15B+35))=0


We calculate terms in parentheses: -((+6B^2-14B-15B+35)), so:

(+6B^2-14B-15B+35)

We get rid of parentheses

6B^2-14B-15B+35

We add all the numbers together, and all the variables

6B^2-29B+35

Back to the equation:

-(6B^2-29B+35)


We get rid of parentheses

-6B^2+29B-35=0

a = -6; b = 29; c = -35;
Δ = b2-4ac
Δ = 292-4·(-6)·(-35)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-1}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+1}{2*-6}=\frac{-28}{-12}
=2+1/3
$