4=10x+.5(10)x^2

Solution for 4=10x+.5(10)x^2 equation:

4=10x+.5(10)x^2

We move all terms to the left:

4-(10x+.5(10)x^2)=0

We get rid of parentheses

-.510x^2-10x+4=0

We add all the numbers together, and all the variables

-0.51x^2-10x+4=0

a = -0.51; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-0.51)·4
Δ = 108.16
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{-(-10)-\sqrt{108.16}}{2*-0.51}=\frac{10-\sqrt{108.16}}{-1.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{108.16}}{2*-0.51}=\frac{10+\sqrt{108.16}}{-1.02}
$