8x2-31x=4

Solution for 8x2-31x=4 equation:

8x^2-31x=4

We move all terms to the left:

8x^2-31x-(4)=0

a = 8; b = -31; c = -4;
Δ = b2-4ac
Δ = -312-4·8·(-4)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-33}{2*8}=\frac{-2}{16}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+33}{2*8}=\frac{64}{16}
=4
$