4x^2+26x=-15

Solution for 4x^2+26x=-15 equation:

4x^2+26x=-15

We move all terms to the left:

4x^2+26x-(-15)=0

We add all the numbers together, and all the variables

4x^2+26x+15=0

a = 4; b = 26; c = +15;
Δ = b2-4ac
Δ = 262-4·4·15
Δ = 436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{109}}{2*4}=\frac{-26-2\sqrt{109}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{109}}{2*4}=\frac{-26+2\sqrt{109}}{8}
$