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

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

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

We move all terms to the left:

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


Domain of the equation: 4x-13)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


3x*4x-13*4x-17*4x-90*4x+3=0

Wy multiply elements

12x^2-52x-68x-360x+3=0

We add all the numbers together, and all the variables

12x^2-480x+3=0

a = 12; b = -480; c = +3;
Δ = b2-4ac
Δ = -4802-4·12·3
Δ = 230256
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:

$\sqrt{\Delta}=\sqrt{230256}=\sqrt{144*1599}=\sqrt{144}*\sqrt{1599}=12\sqrt{1599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-12\sqrt{1599}}{2*12}=\frac{480-12\sqrt{1599}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+12\sqrt{1599}}{2*12}=\frac{480+12\sqrt{1599}}{24}
$