5x^2+46x=105

Solution for 5x^2+46x=105 equation:

5x^2+46x=105

We move all terms to the left:

5x^2+46x-(105)=0

a = 5; b = 46; c = -105;
Δ = b2-4ac
Δ = 462-4·5·(-105)
Δ = 4216
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:

$\sqrt{\Delta}=\sqrt{4216}=\sqrt{4*1054}=\sqrt{4}*\sqrt{1054}=2\sqrt{1054}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{1054}}{2*5}=\frac{-46-2\sqrt{1054}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{1054}}{2*5}=\frac{-46+2\sqrt{1054}}{10}
$