-7x=-3/4x-5

Solution for -7x=-3/4x-5 equation:

-7x=-3/4x-5

We move all terms to the left:

-7x-(-3/4x-5)=0


Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

-7x+3/4x+5=0

We multiply all the terms by the denominator


-7x*4x+5*4x+3=0

Wy multiply elements

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

a = -28; b = 20; c = +3;
Δ = b2-4ac
Δ = 202-4·(-28)·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{46}}{2*-28}=\frac{-20-4\sqrt{46}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{46}}{2*-28}=\frac{-20+4\sqrt{46}}{-56}
$