27=4x^2+5x+7

Solution for 27=4x^2+5x+7 equation:

27=4x^2+5x+7

We move all terms to the left:

27-(4x^2+5x+7)=0

We get rid of parentheses

-4x^2-5x-7+27=0

We add all the numbers together, and all the variables

-4x^2-5x+20=0

a = -4; b = -5; c = +20;
Δ = b2-4ac
Δ = -52-4·(-4)·20
Δ = 345
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{-(-5)-\sqrt{345}}{2*-4}=\frac{5-\sqrt{345}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{345}}{2*-4}=\frac{5+\sqrt{345}}{-8}
$