3/4x+13=5x-21

Solution for 3/4x+13=5x-21 equation:

3/4x+13=5x-21

We move all terms to the left:

3/4x+13-(5x-21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-5x+21+13=0

We multiply all the terms by the denominator


-5x*4x+21*4x+13*4x+3=0

Wy multiply elements

-20x^2+84x+52x+3=0

We add all the numbers together, and all the variables

-20x^2+136x+3=0

a = -20; b = 136; c = +3;
Δ = b2-4ac
Δ = 1362-4·(-20)·3
Δ = 18736
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:

$\sqrt{\Delta}=\sqrt{18736}=\sqrt{16*1171}=\sqrt{16}*\sqrt{1171}=4\sqrt{1171}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-4\sqrt{1171}}{2*-20}=\frac{-136-4\sqrt{1171}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+4\sqrt{1171}}{2*-20}=\frac{-136+4\sqrt{1171}}{-40}
$