0.75x^2=3x+10

Solution for 0.75x^2=3x+10 equation:

0.75x^2=3x+10

We move all terms to the left:

0.75x^2-(3x+10)=0

We get rid of parentheses

0.75x^2-3x-10=0

a = 0.75; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·0.75·(-10)
Δ = 39
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{-(-3)-\sqrt{39}}{2*0.75}=\frac{3-\sqrt{39}}{1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{39}}{2*0.75}=\frac{3+\sqrt{39}}{1.5}
$