3x^2+6x-45=-25x-53

Solution for 3x^2+6x-45=-25x-53 equation:

3x^2+6x-45=-25x-53

We move all terms to the left:

3x^2+6x-45-(-25x-53)=0

We get rid of parentheses

3x^2+6x+25x+53-45=0

We add all the numbers together, and all the variables

3x^2+31x+8=0

a = 3; b = 31; c = +8;
Δ = b2-4ac
Δ = 312-4·3·8
Δ = 865
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{-(31)-\sqrt{865}}{2*3}=\frac{-31-\sqrt{865}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{865}}{2*3}=\frac{-31+\sqrt{865}}{6}
$