5x(83/4)=26/7

Solution for 5x(83/4)=26/7 equation:

5x(83/4)=26/7

We move all terms to the left:

5x(83/4)-(26/7)=0

We add all the numbers together, and all the variables

5x(+83/4)-(+26/7)=0

We multiply parentheses

415x^2-(+26/7)=0

We get rid of parentheses

415x^2-26/7=0

We multiply all the terms by the denominator


415x^2*7-26=0

Wy multiply elements

2905x^2-26=0

a = 2905; b = 0; c = -26;
Δ = b2-4ac
Δ = 02-4·2905·(-26)
Δ = 302120
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:

$\sqrt{\Delta}=\sqrt{302120}=\sqrt{4*75530}=\sqrt{4}*\sqrt{75530}=2\sqrt{75530}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{75530}}{2*2905}=\frac{0-2\sqrt{75530}}{5810}
=-\frac{2\sqrt{75530}}{5810}
=-\frac{\sqrt{75530}}{2905}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{75530}}{2*2905}=\frac{0+2\sqrt{75530}}{5810}
=\frac{2\sqrt{75530}}{5810}
=\frac{\sqrt{75530}}{2905}
$