100=15x+4x^2/2

Solution for 100=15x+4x^2/2 equation:

100=15x+4x^2/2

We move all terms to the left:

100-(15x+4x^2/2)=0

We get rid of parentheses

-4x^2/2-15x+100=0

We multiply all the terms by the denominator


-4x^2-15x*2+100*2=0

We add all the numbers together, and all the variables

-4x^2-15x*2+200=0

Wy multiply elements

-4x^2-30x+200=0

a = -4; b = -30; c = +200;
Δ = b2-4ac
Δ = -302-4·(-4)·200
Δ = 4100
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:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{41}}{2*-4}=\frac{30-10\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{41}}{2*-4}=\frac{30+10\sqrt{41}}{-8}
$