-3x^2-5x+30=7x-10

Solution for -3x^2-5x+30=7x-10 equation:

-3x^2-5x+30=7x-10

We move all terms to the left:

-3x^2-5x+30-(7x-10)=0

We get rid of parentheses

-3x^2-5x-7x+10+30=0

We add all the numbers together, and all the variables

-3x^2-12x+40=0

a = -3; b = -12; c = +40;
Δ = b2-4ac
Δ = -122-4·(-3)·40
Δ = 624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{39}}{2*-3}=\frac{12-4\sqrt{39}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{39}}{2*-3}=\frac{12+4\sqrt{39}}{-6}
$