7x+10=1/2x+1

Solution for 7x+10=1/2x+1 equation:

7x+10=1/2x+1

We move all terms to the left:

7x+10-(1/2x+1)=0


Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

7x-1/2x-1+10=0

We multiply all the terms by the denominator


7x*2x-1*2x+10*2x-1=0

Wy multiply elements

14x^2-2x+20x-1=0

We add all the numbers together, and all the variables

14x^2+18x-1=0

a = 14; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·14·(-1)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{95}}{2*14}=\frac{-18-2\sqrt{95}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{95}}{2*14}=\frac{-18+2\sqrt{95}}{28}
$