4x^2=39x+10

Solution for 4x^2=39x+10 equation:

4x^2=39x+10

We move all terms to the left:

4x^2-(39x+10)=0

We get rid of parentheses

4x^2-39x-10=0

a = 4; b = -39; c = -10;
Δ = b2-4ac
Δ = -392-4·4·(-10)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-41}{2*4}=\frac{-2}{8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+41}{2*4}=\frac{80}{8}
=10
$