1478=x^2+3x

Solution for 1478=x^2+3x equation:

1478=x^2+3x

We move all terms to the left:

1478-(x^2+3x)=0

We get rid of parentheses

-x^2-3x+1478=0

We add all the numbers together, and all the variables

-1x^2-3x+1478=0

a = -1; b = -3; c = +1478;
Δ = b2-4ac
Δ = -32-4·(-1)·1478
Δ = 5921
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{-(-3)-\sqrt{5921}}{2*-1}=\frac{3-\sqrt{5921}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5921}}{2*-1}=\frac{3+\sqrt{5921}}{-2}
$