1/2x+40=4x-15

Solution for 1/2x+40=4x-15 equation:

1/2x+40=4x-15

We move all terms to the left:

1/2x+40-(4x-15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-4x+15+40=0

We multiply all the terms by the denominator


-4x*2x+15*2x+40*2x+1=0

Wy multiply elements

-8x^2+30x+80x+1=0

We add all the numbers together, and all the variables

-8x^2+110x+1=0

a = -8; b = 110; c = +1;
Δ = b2-4ac
Δ = 1102-4·(-8)·1
Δ = 12132
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:

$\sqrt{\Delta}=\sqrt{12132}=\sqrt{36*337}=\sqrt{36}*\sqrt{337}=6\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-6\sqrt{337}}{2*-8}=\frac{-110-6\sqrt{337}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+6\sqrt{337}}{2*-8}=\frac{-110+6\sqrt{337}}{-16}
$