3x^2+10=15x+20

Solution for 3x^2+10=15x+20 equation:

3x^2+10=15x+20

We move all terms to the left:

3x^2+10-(15x+20)=0

We get rid of parentheses

3x^2-15x-20+10=0

We add all the numbers together, and all the variables

3x^2-15x-10=0

a = 3; b = -15; c = -10;
Δ = b2-4ac
Δ = -152-4·3·(-10)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{345}}{2*3}=\frac{15-\sqrt{345}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{345}}{2*3}=\frac{15+\sqrt{345}}{6}
$