2x+14=4/5x+7

Solution for 2x+14=4/5x+7 equation:

2x+14=4/5x+7

We move all terms to the left:

2x+14-(4/5x+7)=0


Domain of the equation: 5x+7)!=0

x∈R


We get rid of parentheses

2x-4/5x-7+14=0

We multiply all the terms by the denominator


2x*5x-7*5x+14*5x-4=0

Wy multiply elements

10x^2-35x+70x-4=0

We add all the numbers together, and all the variables

10x^2+35x-4=0

a = 10; b = 35; c = -4;
Δ = b2-4ac
Δ = 352-4·10·(-4)
Δ = 1385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1385}}{2*10}=\frac{-35-\sqrt{1385}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1385}}{2*10}=\frac{-35+\sqrt{1385}}{20}
$