4x2-31x=-27

Solution for 4x2-31x=-27 equation:

4x^2-31x=-27

We move all terms to the left:

4x^2-31x-(-27)=0

We add all the numbers together, and all the variables

4x^2-31x+27=0

a = 4; b = -31; c = +27;
Δ = b2-4ac
Δ = -312-4·4·27
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{-(-31)-23}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+23}{2*4}=\frac{54}{8}
=6+3/4
$