1.8b(b-5.3)-4.2=5.8(b-2.3)

Solution for 1.8b(b-5.3)-4.2=5.8(b-2.3) equation:

1.8b(b-5.3)-4.2=5.8(b-2.3)

We move all terms to the left:

1.8b(b-5.3)-4.2-(5.8(b-2.3))=0

We multiply parentheses

b^2-5.3b-(5.8(b-2.3))-4.2=0


We calculate terms in parentheses: -(5.8(b-2.3)), so:

5.8(b-2.3)

We multiply parentheses

5.8b-13.34

Back to the equation:

-(5.8b-13.34)


We get rid of parentheses

b^2-5.3b-5.8b+13.34-4.2=0

We add all the numbers together, and all the variables

b^2-11.1b+9.14=0

a = 1; b = -11.1; c = +9.14;
Δ = b2-4ac
Δ = -11.12-4·1·9.14
Δ = 86.65
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{-(-11.1)-\sqrt{86.65}}{2*1}=\frac{11.1-\sqrt{86.65}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.1)+\sqrt{86.65}}{2*1}=\frac{11.1+\sqrt{86.65}}{2}
$