12x^2-70x=7

Solution for 12x^2-70x=7 equation:

12x^2-70x=7

We move all terms to the left:

12x^2-70x-(7)=0

a = 12; b = -70; c = -7;
Δ = b2-4ac
Δ = -702-4·12·(-7)
Δ = 5236
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:

$\sqrt{\Delta}=\sqrt{5236}=\sqrt{4*1309}=\sqrt{4}*\sqrt{1309}=2\sqrt{1309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1309}}{2*12}=\frac{70-2\sqrt{1309}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1309}}{2*12}=\frac{70+2\sqrt{1309}}{24}
$