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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(2B(5B-3)-7), so:

2B(5B-3)-7

We multiply parentheses

10B^2-6B-7

Back to the equation:

-(10B^2-6B-7)


We get rid of parentheses

-10B^2+B+6B+7=0

We add all the numbers together, and all the variables

-10B^2+7B+7=0

a = -10; b = 7; c = +7;
Δ = b2-4ac
Δ = 72-4·(-10)·7
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{329}}{2*-10}=\frac{-7-\sqrt{329}}{-20}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{329}}{2*-10}=\frac{-7+\sqrt{329}}{-20}
$