5x^2+3x-x^2+7x=111

Solution for 5x^2+3x-x^2+7x=111 equation:

5x^2+3x-x^2+7x=111

We move all terms to the left:

5x^2+3x-x^2+7x-(111)=0

We add all the numbers together, and all the variables

4x^2+10x-111=0

a = 4; b = 10; c = -111;
Δ = b2-4ac
Δ = 102-4·4·(-111)
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{469}}{2*4}=\frac{-10-2\sqrt{469}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{469}}{2*4}=\frac{-10+2\sqrt{469}}{8}
$