(x2-19)/10=4

Solution for (x2-19)/10=4 equation:

(x2-19)/10=4

We move all terms to the left:

(x2-19)/10-(4)=0

We add all the numbers together, and all the variables

(+x^2-19)/10-4=0

We multiply all the terms by the denominator


(+x^2-19)-4*10=0

We add all the numbers together, and all the variables

(+x^2-19)-40=0

We get rid of parentheses

x^2-19-40=0

We add all the numbers together, and all the variables

x^2-59=0

a = 1; b = 0; c = -59;
Δ = b2-4ac
Δ = 02-4·1·(-59)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{59}}{2*1}=\frac{0-2\sqrt{59}}{2}
=-\frac{2\sqrt{59}}{2}
=-\sqrt{59}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{59}}{2*1}=\frac{0+2\sqrt{59}}{2}
=\frac{2\sqrt{59}}{2}
=\sqrt{59}
$