3/4x-2(3x+2)=-25

Solution for 3/4x-2(3x+2)=-25 equation:

3/4x-2(3x+2)=-25

We move all terms to the left:

3/4x-2(3x+2)-(-25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-2(3x+2)+25=0

We multiply parentheses

3/4x-6x-4+25=0

We multiply all the terms by the denominator


-6x*4x-4*4x+25*4x+3=0

Wy multiply elements

-24x^2-16x+100x+3=0

We add all the numbers together, and all the variables

-24x^2+84x+3=0

a = -24; b = 84; c = +3;
Δ = b2-4ac
Δ = 842-4·(-24)·3
Δ = 7344
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:

$\sqrt{\Delta}=\sqrt{7344}=\sqrt{144*51}=\sqrt{144}*\sqrt{51}=12\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{51}}{2*-24}=\frac{-84-12\sqrt{51}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{51}}{2*-24}=\frac{-84+12\sqrt{51}}{-48}
$