8x+3=4.7x(2.8x+3.7)

Solution for 8x+3=4.7x(2.8x+3.7) equation:

8x+3=4.7x(2.8x+3.7)

We move all terms to the left:

8x+3-(4.7x(2.8x+3.7))=0


We calculate terms in parentheses: -(4.7x(2.8x+3.7)), so:

4.7x(2.8x+3.7)

We multiply parentheses

8x^2+14.8x

Back to the equation:

-(8x^2+14.8x)


We get rid of parentheses

-8x^2+8x-14.8x+3=0

We add all the numbers together, and all the variables

-8x^2-6.8x+3=0

a = -8; b = -6.8; c = +3;
Δ = b2-4ac
Δ = -6.82-4·(-8)·3
Δ = 142.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6.8)-\sqrt{142.24}}{2*-8}=\frac{6.8-\sqrt{142.24}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.8)+\sqrt{142.24}}{2*-8}=\frac{6.8+\sqrt{142.24}}{-16}
$