3x-40=1/2x+35

Solution for 3x-40=1/2x+35 equation:

3x-40=1/2x+35

We move all terms to the left:

3x-40-(1/2x+35)=0


Domain of the equation: 2x+35)!=0

x∈R


We get rid of parentheses

3x-1/2x-35-40=0

We multiply all the terms by the denominator


3x*2x-35*2x-40*2x-1=0

Wy multiply elements

6x^2-70x-80x-1=0

We add all the numbers together, and all the variables

6x^2-150x-1=0

a = 6; b = -150; c = -1;
Δ = b2-4ac
Δ = -1502-4·6·(-1)
Δ = 22524
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:

$\sqrt{\Delta}=\sqrt{22524}=\sqrt{4*5631}=\sqrt{4}*\sqrt{5631}=2\sqrt{5631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5631}}{2*6}=\frac{150-2\sqrt{5631}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5631}}{2*6}=\frac{150+2\sqrt{5631}}{12}
$