7x^2-6x=142

Solution for 7x^2-6x=142 equation:

7x^2-6x=142

We move all terms to the left:

7x^2-6x-(142)=0

a = 7; b = -6; c = -142;
Δ = b2-4ac
Δ = -62-4·7·(-142)
Δ = 4012
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:

$\sqrt{\Delta}=\sqrt{4012}=\sqrt{4*1003}=\sqrt{4}*\sqrt{1003}=2\sqrt{1003}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1003}}{2*7}=\frac{6-2\sqrt{1003}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1003}}{2*7}=\frac{6+2\sqrt{1003}}{14}
$