(18+24)5-8x=2x+16*90/42x

Solution for (18+24)5-8x=2x+16*90/42x equation:

(18+24)5-8x=2x+16*90/42x

We move all terms to the left:

(18+24)5-8x-(2x+16*90/42x)=0


Domain of the equation: 42x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-8x-(+2x+16*90/42x)+425=0

We get rid of parentheses

-8x-2x-16*90/42x+425=0

We multiply all the terms by the denominator


-8x*42x-2x*42x+425*42x-16*90=0

We add all the numbers together, and all the variables

-8x*42x-2x*42x+425*42x-1440=0

Wy multiply elements

-336x^2-84x^2+17850x-1440=0

We add all the numbers together, and all the variables

-420x^2+17850x-1440=0

a = -420; b = 17850; c = -1440;
Δ = b2-4ac
Δ = 178502-4·(-420)·(-1440)
Δ = 316203300
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:

$\sqrt{\Delta}=\sqrt{316203300}=\sqrt{900*351337}=\sqrt{900}*\sqrt{351337}=30\sqrt{351337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17850)-30\sqrt{351337}}{2*-420}=\frac{-17850-30\sqrt{351337}}{-840}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17850)+30\sqrt{351337}}{2*-420}=\frac{-17850+30\sqrt{351337}}{-840}
$