3x-5x+45=34x^2+2x-50-30

Solution for 3x-5x+45=34x^2+2x-50-30 equation:

3x-5x+45=34x^2+2x-50-30

We move all terms to the left:

3x-5x+45-(34x^2+2x-50-30)=0

We add all the numbers together, and all the variables

-2x-(34x^2+2x-50-30)+45=0

We get rid of parentheses

-34x^2-2x-2x+50+30+45=0

We add all the numbers together, and all the variables

-34x^2-4x+125=0

a = -34; b = -4; c = +125;
Δ = b2-4ac
Δ = -42-4·(-34)·125
Δ = 17016
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:

$\sqrt{\Delta}=\sqrt{17016}=\sqrt{4*4254}=\sqrt{4}*\sqrt{4254}=2\sqrt{4254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{4254}}{2*-34}=\frac{4-2\sqrt{4254}}{-68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{4254}}{2*-34}=\frac{4+2\sqrt{4254}}{-68}
$