(3/4)x-13+3x-17=90

Solution for (3/4)x-13+3x-17=90 equation:

(3/4)x-13+3x-17=90

We move all terms to the left:

(3/4)x-13+3x-17-(90)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)x+3x-13-17-90=0

We add all the numbers together, and all the variables

3x+(+3/4)x-120=0

We multiply parentheses

3x^2+3x-120=0

a = 3; b = 3; c = -120;
Δ = b2-4ac
Δ = 32-4·3·(-120)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{161}}{2*3}=\frac{-3-3\sqrt{161}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{161}}{2*3}=\frac{-3+3\sqrt{161}}{6}
$