4b^2-7b+5=1+3b

Solution for 4b^2-7b+5=1+3b equation:

4b^2-7b+5=1+3b

We move all terms to the left:

4b^2-7b+5-(1+3b)=0

We add all the numbers together, and all the variables

4b^2-7b-(3b+1)+5=0

We get rid of parentheses

4b^2-7b-3b-1+5=0

We add all the numbers together, and all the variables

4b^2-10b+4=0

a = 4; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·4·4
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*4}=\frac{4}{8}
=1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*4}=\frac{16}{8}
=2
$