3x^2+12x-53=10

Solution for 3x^2+12x-53=10 equation:

3x^2+12x-53=10

We move all terms to the left:

3x^2+12x-53-(10)=0

We add all the numbers together, and all the variables

3x^2+12x-63=0

a = 3; b = 12; c = -63;
Δ = b2-4ac
Δ = 122-4·3·(-63)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-30}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+30}{2*3}=\frac{18}{6}
=3
$