-7,5x^2+65,3x-142=0

Solution for -7,5x^2+65,3x-142=0 equation:

-7.5x^2+65.3x-142=0

a = -7.5; b = 65.3; c = -142;
Δ = b2-4ac
Δ = 65.32-4·(-7.5)·(-142)
Δ = 4.0899999999992
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{-(65.3)-\sqrt{4.0899999999992}}{2*-7.5}=\frac{-65.3-\sqrt{4.0899999999992}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65.3)+\sqrt{4.0899999999992}}{2*-7.5}=\frac{-65.3+\sqrt{4.0899999999992}}{-15}
$