3x+7x2=45

Solution for 3x+7x2=45 equation:

3x+7x^2=45

We move all terms to the left:

3x+7x^2-(45)=0

a = 7; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·7·(-45)
Δ = 1269
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:

$\sqrt{\Delta}=\sqrt{1269}=\sqrt{9*141}=\sqrt{9}*\sqrt{141}=3\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{141}}{2*7}=\frac{-3-3\sqrt{141}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{141}}{2*7}=\frac{-3+3\sqrt{141}}{14}
$