x=52x^2-3x+4x-7

Solution for x=52x^2-3x+4x-7 equation:

x=52x^2-3x+4x-7

We move all terms to the left:

x-(52x^2-3x+4x-7)=0

We get rid of parentheses

-52x^2+x+3x-4x+7=0

We add all the numbers together, and all the variables

-52x^2+7=0

a = -52; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-52)·7
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{91}}{2*-52}=\frac{0-4\sqrt{91}}{-104}
=-\frac{4\sqrt{91}}{-104}
=-\frac{\sqrt{91}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{91}}{2*-52}=\frac{0+4\sqrt{91}}{-104}
=\frac{4\sqrt{91}}{-104}
=\frac{\sqrt{91}}{-26}
$