X^2-7x-10=20-3x^2

Solution for X^2-7x-10=20-3x^2 equation:

X^2-7X-10=20-3X^2

We move all terms to the left:

X^2-7X-10-(20-3X^2)=0

We get rid of parentheses

X^2+3X^2-7X-20-10=0

We add all the numbers together, and all the variables

4X^2-7X-30=0

a = 4; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·4·(-30)
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{-(-7)-23}{2*4}=\frac{-16}{8}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*4}=\frac{30}{8}
=3+3/4
$