4x^2+25x=-6

Solution for 4x^2+25x=-6 equation:

4x^2+25x=-6

We move all terms to the left:

4x^2+25x-(-6)=0

We add all the numbers together, and all the variables

4x^2+25x+6=0

a = 4; b = 25; c = +6;
Δ = b2-4ac
Δ = 252-4·4·6
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-23}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+23}{2*4}=\frac{-2}{8}
=-1/4
$