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

Solution for -(x-3)+3/4x+5=0 equation:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+12x+20x+3=0

We add all the numbers together, and all the variables

-4x^2+32x+3=0

a = -4; b = 32; c = +3;
Δ = b2-4ac
Δ = 322-4·(-4)·3
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{67}}{2*-4}=\frac{-32-4\sqrt{67}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{67}}{2*-4}=\frac{-32+4\sqrt{67}}{-8}
$