8x+2=4x+105)14x+4=5x+31

Solution for 8x+2=4x+105)14x+4=5x+31 equation:

8x+2=4x+105)14x+4=5x+31

We move all terms to the left:

8x+2-(4x+105)14x+4)=0

We add all the numbers together, and all the variables

8x-(4x+105)14x=0

We multiply parentheses

-56x^2+8x-1470x=0

We add all the numbers together, and all the variables

-56x^2-1462x=0

a = -56; b = -1462; c = 0;
Δ = b2-4ac
Δ = -14622-4·(-56)·0
Δ = 2137444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2137444}=1462$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1462)-1462}{2*-56}=\frac{0}{-112}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1462)+1462}{2*-56}=\frac{2924}{-112}
=-26+3/28
$