5.2x-7=3/4x+14

Solution for 5.2x-7=3/4x+14 equation:

5.2x-7=3/4x+14

We move all terms to the left:

5.2x-7-(3/4x+14)=0


Domain of the equation: 4x+14)!=0

x∈R


We get rid of parentheses

5.2x-3/4x-14-7=0

We multiply all the terms by the denominator


(5.2x)*4x-14*4x-7*4x-3=0

We add all the numbers together, and all the variables

(+5.2x)*4x-14*4x-7*4x-3=0

We multiply parentheses

20x^2-14*4x-7*4x-3=0

Wy multiply elements

20x^2-56x-28x-3=0

We add all the numbers together, and all the variables

20x^2-84x-3=0

a = 20; b = -84; c = -3;
Δ = b2-4ac
Δ = -842-4·20·(-3)
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-8\sqrt{114}}{2*20}=\frac{84-8\sqrt{114}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+8\sqrt{114}}{2*20}=\frac{84+8\sqrt{114}}{40}
$