-7v^2+42=45v

Solution for -7v^2+42=45v equation:

-7v^2+42=45v

We move all terms to the left:

-7v^2+42-(45v)=0

a = -7; b = -45; c = +42;
Δ = b2-4ac
Δ = -452-4·(-7)·42
Δ = 3201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{3201}}{2*-7}=\frac{45-\sqrt{3201}}{-14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{3201}}{2*-7}=\frac{45+\sqrt{3201}}{-14}
$