3/4x+11=2x-10

Solution for 3/4x+11=2x-10 equation:

3/4x+11=2x-10

We move all terms to the left:

3/4x+11-(2x-10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-2x+10+11=0

We multiply all the terms by the denominator


-2x*4x+10*4x+11*4x+3=0

Wy multiply elements

-8x^2+40x+44x+3=0

We add all the numbers together, and all the variables

-8x^2+84x+3=0

a = -8; b = 84; c = +3;
Δ = b2-4ac
Δ = 842-4·(-8)·3
Δ = 7152
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:

$\sqrt{\Delta}=\sqrt{7152}=\sqrt{16*447}=\sqrt{16}*\sqrt{447}=4\sqrt{447}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{447}}{2*-8}=\frac{-84-4\sqrt{447}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{447}}{2*-8}=\frac{-84+4\sqrt{447}}{-16}
$