275x^2+37x-17x+7=572x^2+85x+19x-12

Solution for 275x^2+37x-17x+7=572x^2+85x+19x-12 equation:

275x^2+37x-17x+7=572x^2+85x+19x-12

We move all terms to the left:

275x^2+37x-17x+7-(572x^2+85x+19x-12)=0

We add all the numbers together, and all the variables

275x^2+20x-(572x^2+85x+19x-12)+7=0

We get rid of parentheses

275x^2-572x^2+20x-85x-19x+12+7=0

We add all the numbers together, and all the variables

-297x^2-84x+19=0

a = -297; b = -84; c = +19;
Δ = b2-4ac
Δ = -842-4·(-297)·19
Δ = 29628
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:

$\sqrt{\Delta}=\sqrt{29628}=\sqrt{36*823}=\sqrt{36}*\sqrt{823}=6\sqrt{823}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-6\sqrt{823}}{2*-297}=\frac{84-6\sqrt{823}}{-594}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+6\sqrt{823}}{2*-297}=\frac{84+6\sqrt{823}}{-594}
$