3a^2-15a-10=5a-3

Solution for 3a^2-15a-10=5a-3 equation:

3a^2-15a-10=5a-3

We move all terms to the left:

3a^2-15a-10-(5a-3)=0

We get rid of parentheses

3a^2-15a-5a+3-10=0

We add all the numbers together, and all the variables

3a^2-20a-7=0

a = 3; b = -20; c = -7;
Δ = b2-4ac
Δ = -202-4·3·(-7)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-22}{2*3}=\frac{-2}{6}
=-1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+22}{2*3}=\frac{42}{6}
=7
$