3.1x(2x+7)+-6.2x^2=19.53

Solution for 3.1x(2x+7)+-6.2x^2=19.53 equation:

3.1x(2x+7)+-6.2x^2=19.53

We move all terms to the left:

3.1x(2x+7)+-6.2x^2-(19.53)=0

We add all the numbers together, and all the variables

-6.2x^2+3.1x(2x+7)-19.53=0

We multiply parentheses

-6.2x^2+6x^2+21x-19.53=0

We add all the numbers together, and all the variables

-0.2x^2+21x-19.53=0

a = -0.2; b = 21; c = -19.53;
Δ = b2-4ac
Δ = 212-4·(-0.2)·(-19.53)
Δ = 425.376
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)-\sqrt{425.376}}{2*-0.2}=\frac{-21-\sqrt{425.376}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{425.376}}{2*-0.2}=\frac{-21+\sqrt{425.376}}{-0.4}
$