(5x+7)2=17x2+84x+46

Solution for (5x+7)2=17x2+84x+46 equation:

(5x+7)2=17x^2+84x+46

We move all terms to the left:

(5x+7)2-(17x^2+84x+46)=0

We multiply parentheses

10x-(17x^2+84x+46)+14=0

We get rid of parentheses

-17x^2+10x-84x-46+14=0

We add all the numbers together, and all the variables

-17x^2-74x-32=0

a = -17; b = -74; c = -32;
Δ = b2-4ac
Δ = -742-4·(-17)·(-32)
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-10\sqrt{33}}{2*-17}=\frac{74-10\sqrt{33}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+10\sqrt{33}}{2*-17}=\frac{74+10\sqrt{33}}{-34}
$