5x^2=3x+26

Solution for 5x^2=3x+26 equation:

5x^2=3x+26

We move all terms to the left:

5x^2-(3x+26)=0

We get rid of parentheses

5x^2-3x-26=0

a = 5; b = -3; c = -26;
Δ = b2-4ac
Δ = -32-4·5·(-26)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-23}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+23}{2*5}=\frac{26}{10}
=2+3/5
$