3.1x+6.2-1.5x=5.2x(x-4)

Solution for 3.1x+6.2-1.5x=5.2x(x-4) equation:

3.1x+6.2-1.5x=5.2x(x-4)

We move all terms to the left:

3.1x+6.2-1.5x-(5.2x(x-4))=0

We add all the numbers together, and all the variables

1.6x-(5.2x(x-4))+6.2=0


We calculate terms in parentheses: -(5.2x(x-4)), so:

5.2x(x-4)

We multiply parentheses

5x^2-20x

Back to the equation:

-(5x^2-20x)


We get rid of parentheses

-5x^2+1.6x+20x+6.2=0

We add all the numbers together, and all the variables

-5x^2+21.6x+6.2=0

a = -5; b = 21.6; c = +6.2;
Δ = b2-4ac
Δ = 21.62-4·(-5)·6.2
Δ = 590.56
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{-(21.6)-\sqrt{590.56}}{2*-5}=\frac{-21.6-\sqrt{590.56}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21.6)+\sqrt{590.56}}{2*-5}=\frac{-21.6+\sqrt{590.56}}{-10}
$