7x^2=64x-60

Solution for 7x^2=64x-60 equation:

7x^2=64x-60

We move all terms to the left:

7x^2-(64x-60)=0

We get rid of parentheses

7x^2-64x+60=0

a = 7; b = -64; c = +60;
Δ = b2-4ac
Δ = -642-4·7·60
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{151}}{2*7}=\frac{64-4\sqrt{151}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{151}}{2*7}=\frac{64+4\sqrt{151}}{14}
$