10x^2-7x-12=52

Solution for 10x^2-7x-12=52 equation:

10x^2-7x-12=52

We move all terms to the left:

10x^2-7x-12-(52)=0

We add all the numbers together, and all the variables

10x^2-7x-64=0

a = 10; b = -7; c = -64;
Δ = b2-4ac
Δ = -72-4·10·(-64)
Δ = 2609
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{-(-7)-\sqrt{2609}}{2*10}=\frac{7-\sqrt{2609}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{2609}}{2*10}=\frac{7+\sqrt{2609}}{20}
$