4x^2+8x+27=88

Solution for 4x^2+8x+27=88 equation:

4x^2+8x+27=88

We move all terms to the left:

4x^2+8x+27-(88)=0

We add all the numbers together, and all the variables

4x^2+8x-61=0

a = 4; b = 8; c = -61;
Δ = b2-4ac
Δ = 82-4·4·(-61)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{65}}{2*4}=\frac{-8-4\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{65}}{2*4}=\frac{-8+4\sqrt{65}}{8}
$