x*(1.07^10)+.2x=4

Solution for x*(1.07^10)+.2x=4 equation:

x(1.07^10)+.2x=4

We move all terms to the left:

x(1.07^10)+.2x-(4)=0

We add all the numbers together, and all the variables

.2x+x(1.07^10)-4=0

We multiply parentheses

x^2+.2x-4=0

a = 1; b = .2; c = -4;
Δ = b2-4ac
Δ = .22-4·1·(-4)
Δ = 16.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(.2)-\sqrt{16.04}}{2*1}=\frac{-0.2-\sqrt{16.04}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(.2)+\sqrt{16.04}}{2*1}=\frac{-0.2+\sqrt{16.04}}{2}
$