10x^2=5x+105

Solution for 10x^2=5x+105 equation:

10x^2=5x+105

We move all terms to the left:

10x^2-(5x+105)=0

We get rid of parentheses

10x^2-5x-105=0

a = 10; b = -5; c = -105;
Δ = b2-4ac
Δ = -52-4·10·(-105)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-65}{2*10}=\frac{-60}{20}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+65}{2*10}=\frac{70}{20}
=3+1/2
$