7x^2+32x-13=54

Solution for 7x^2+32x-13=54 equation:

7x^2+32x-13=54

We move all terms to the left:

7x^2+32x-13-(54)=0

We add all the numbers together, and all the variables

7x^2+32x-67=0

a = 7; b = 32; c = -67;
Δ = b2-4ac
Δ = 322-4·7·(-67)
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-10\sqrt{29}}{2*7}=\frac{-32-10\sqrt{29}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+10\sqrt{29}}{2*7}=\frac{-32+10\sqrt{29}}{14}
$