45x=61x2

Solution for 45x=61x2 equation:

45x=61x^2

We move all terms to the left:

45x-(61x^2)=0

determiningTheFunctionDomain
-61x^2+45x=0

a = -61; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-61)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-61}=\frac{-90}{-122}
=45/61
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-61}=\frac{0}{-122}
=0
$