7x^2-6x=45

Solution for 7x^2-6x=45 equation:

7x^2-6x=45

We move all terms to the left:

7x^2-6x-(45)=0

a = 7; b = -6; c = -45;
Δ = b2-4ac
Δ = -62-4·7·(-45)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-36}{2*7}=\frac{-30}{14}
=-2+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+36}{2*7}=\frac{42}{14}
=3
$