4x2=-12x-7

Solution for 4x2=-12x-7 equation:

4x^2=-12x-7

We move all terms to the left:

4x^2-(-12x-7)=0

We get rid of parentheses

4x^2+12x+7=0

a = 4; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·4·7
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{2}}{2*4}=\frac{-12-4\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{2}}{2*4}=\frac{-12+4\sqrt{2}}{8}
$