10x^2=5x+30

Solution for 10x^2=5x+30 equation:

10x^2=5x+30

We move all terms to the left:

10x^2-(5x+30)=0

We get rid of parentheses

10x^2-5x-30=0

a = 10; b = -5; c = -30;
Δ = b2-4ac
Δ = -52-4·10·(-30)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-35}{2*10}=\frac{-30}{20}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+35}{2*10}=\frac{40}{20}
=2
$